Finite Group Databasebeta

← Group #72228384

Character table — Group #72228384

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122333333336666888888888888888899991818242424242424242424242424242424243232323232323232323232323232323272727272727272727272727272727272
order1222222222222222223366666666666666222222666666666666666633666666666666664444444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ41111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ511-1-11-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ611-1-11-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ711-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ811-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ92222222222222222222-12-122-1-122-1-122-1-122222222-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ10222222222222222222-12-12-1-122-1-122-1-122222222-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ11222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-122-1-122-1-122-1-10000000000000000
χ12222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-1-122-1-122-1-1220000000000000000
χ132222-2-222222222-2-2-2-22-12-122-1-1-2-211-2-2112222-2-222-1-122-1-1-2-211-2-211-1-1-1-1-1-1-1-1111111110000000000000000
χ142222-2-222222222-2-2-2-2-12-12-1-12211-2-211-2-22222-2-2-1-122-1-12211-2-211-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ152222-2-222222222-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-1111111112-12-122-1-1-2-211-2-2110000000000000000
χ162222-2-222222222-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-111111111-12-12-1-12211-2-211-2-20000000000000000
χ1722-2-22-22222-2-2-2-222-2-22-12-1-2-21122-1-1-2-21122-2-22-222-1-1-2-21122-1-1-2-211-1-1-1-11111-1-1-1-111110000000000000000
χ1822-2-22-22222-2-2-2-222-2-2-12-1211-2-2-1-12211-2-222-2-22-2-1-12211-2-2-1-12211-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ1922-2-22-22222-2-2-2-222-2-2-1-1-1-11111-1-1-1-1111122-2-22-2-1-1-1-11111-1-1-1-111112-12-1-2-21122-1-1-2-2110000000000000000
χ2022-2-22-22222-2-2-2-222-2-2-1-1-1-11111-1-1-1-1111122-2-22-2-1-1-1-11111-1-1-1-11111-12-1211-2-2-1-12211-2-20000000000000000
χ2122-2-2-222222-2-2-2-2-2-2222-12-1-2-211-2-21122-1-122-2-2-2222-1-1-2-211-2-21122-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2222-2-2-222222-2-2-2-2-2-222-12-1211-2-211-2-2-1-12222-2-2-22-1-12211-2-211-2-2-1-122-1-1-1-111111111-1-1-1-10000000000000000
χ2322-2-2-222222-2-2-2-2-2-222-1-1-1-111111111-1-1-1-122-2-2-22-1-1-1-111111111-1-1-1-12-12-1-2-211-2-21122-1-10000000000000000
χ2422-2-2-222222-2-2-2-2-2-222-1-1-1-111111111-1-1-1-122-2-2-22-1-1-1-111111111-1-1-1-1-12-1211-2-211-2-2-1-1220000000000000000
χ252-22-20022-2-222-2-2000022-2-22-22-2000000002-22-2002-22-22-22-20000000022-2-22-22-2000000000000000000000000
χ262-22-20022-2-222-2-200002-1-212-2-1100−i3i300−i3i32-22-2002-2-112-2-1100−i3i300−i3i3-1-111-11-11−i3i3−i3i3−i3i3−i3i30000000000000000
χ272-22-20022-2-222-2-200002-1-212-2-1100i3−i300i3−i32-22-2002-2-112-2-1100i3−i300i3−i3-1-111-11-11i3−i3i3−i3i3−i3i3−i30000000000000000
χ282-22-20022-2-222-2-20000-121-2-112-2−i3i300−i3i3002-22-200-112-2-112-2−i3i300−i3i300-1-111-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ292-22-20022-2-222-2-20000-121-2-112-2i3−i300i3−i3002-22-200-112-2-112-2i3−i300i3−i300-1-111-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ302-22-20022-2-222-2-20000-1-111-11-11−i3i3−i3i3−i3i3−i3i32-22-200-11-11-11-11−i3i3−i3i3−i3i3−i3i3-121-2-112-2i3−i300i3−i3000000000000000000
χ312-22-20022-2-222-2-20000-1-111-11-11−i3i3i3−i3−i3i3i3−i32-22-200-11-11-11-11−i3i3i3−i3−i3i3i3−i32-1-212-2-1100−i3i300−i3i30000000000000000
χ322-22-20022-2-222-2-20000-1-111-11-11i3−i3−i3i3i3−i3−i3i32-22-200-11-11-11-11i3−i3−i3i3i3−i3−i3i32-1-212-2-1100i3−i300i3−i30000000000000000
χ332-22-20022-2-222-2-20000-1-111-11-11i3−i3i3−i3i3−i3i3−i32-22-200-11-11-11-11i3−i3i3−i3i3−i3i3−i3-121-2-112-2−i3i300−i3i3000000000000000000
χ342-2-220022-2-2-2-222000022-2-2-22-22000000002-2-22002-22-2-22-220000000022-2-2-22-22000000000000000000000000
χ352-2-220022-2-2-2-22200002-1-21-221-100−i3i300i3−i32-2-22002-2-11-221-100−i3i300i3−i3-1-1111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ362-2-220022-2-2-2-22200002-1-21-221-100i3−i300−i3i32-2-22002-2-11-221-100i3−i300−i3i3-1-1111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ372-2-220022-2-2-2-2220000-121-21-1-22−i3i300i3−i3002-2-2200-112-21-1-22−i3i300i3−i300-1-1111-11-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ382-2-220022-2-2-2-2220000-121-21-1-22i3−i300−i3i3002-2-2200-112-21-1-22i3−i300−i3i300-1-1111-11-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ392-2-220022-2-2-2-2220000-1-1111-11-1−i3i3−i3i3i3−i3i3−i32-2-2200-11-111-11-1−i3i3−i3i3i3−i3i3−i3-121-21-1-22i3−i300−i3i3000000000000000000
χ402-2-220022-2-2-2-2220000-1-1111-11-1−i3i3i3−i3i3−i3−i3i32-2-2200-11-111-11-1−i3i3i3−i3i3−i3−i3i32-1-21-221-100−i3i300i3−i30000000000000000
χ412-2-220022-2-2-2-2220000-1-1111-11-1i3−i3−i3i3−i3i3i3−i32-2-2200-11-111-11-1i3−i3−i3i3−i3i3i3−i32-1-21-221-100i3−i300−i3i30000000000000000
χ422-2-220022-2-2-2-2220000-1-1111-11-1i3−i3i3−i3−i3i3−i3i32-2-2200-11-111-11-1i3−i3i3−i3−i3i3−i3i3-121-21-1-22−i3i300i3−i3000000000000000000
χ433333333-13-13-13-13-13-10303003300330033-1-1-1-1-1-100-1-100-1-100-1-100-1-1000000000000000011111-11-11-11-1-1-1-1-1
χ443333333-13-13-13-13-13-10303003300330033-1-1-1-1-1-100-1-100-1-100-1-100-1-10000000000000000-1-1-1-1-11-11-11-111111
χ45333333-13-13-13-13-13-133030330033003300-1-1-1-1-1-1-1-100-1-100-1-100-1-10000000000000000001111-11-11-11-11-1-1-1-1
χ46333333-13-13-13-13-13-133030330033003300-1-1-1-1-1-1-1-100-1-100-1-100-1-1000000000000000000-1-1-1-11-11-11-11-11111
χ473333-3-33-13-13-13-1-31-310303003300-3-300-3-3-1-1-1-11100-1-100-1-100110011000000000000000011-1-11-11-1-11-11-1-111
χ483333-3-33-13-13-13-1-31-310303003300-3-300-3-3-1-1-1-11100-1-100-1-1001100110000000000000000-1-111-11-111-11-111-1-1
χ493333-3-3-13-13-13-131-31-330303300-3-300-3-300-1-1-1-111-1-100-1-10011001100000000000000000011-1-1-11-111-11-1-1-111
χ503333-3-3-13-13-13-131-31-330303300-3-300-3-300-1-1-1-111-1-100-1-100110011000000000000000000-1-1111-11-1-11-1111-1-1
χ5133-3-33-33-13-1-31-313-1-31030300-3-3003300-3-3-1-111-1100-1-1001100-1-100110000000000000000i−ii−ii−i−iii−i−ii−ii−ii
χ5233-3-33-33-13-1-31-313-1-31030300-3-3003300-3-3-1-111-1100-1-1001100-1-100110000000000000000−ii−ii−iii−i−iii−ii−ii−i
χ5333-3-33-3-13-131-31-3-131-33030-3-3003300-3-300-1-111-11-1-1001100-1-10011000000000000000000i−ii−i−iii−i−iii−i−ii−ii
χ5433-3-33-3-13-131-31-3-131-33030-3-3003300-3-300-1-111-11-1-1001100-1-10011000000000000000000−ii−iii−i−iii−i−iii−ii−i
χ5533-3-3-333-13-1-31-31-313-1030300-3-300-3-30033-1-1111-100-1-10011001100-1-10000000000000000i−i−iii−i−ii−iii−i−iii−i
χ5633-3-3-333-13-1-31-31-313-1030300-3-300-3-30033-1-1111-100-1-10011001100-1-10000000000000000−iii−i−iii−ii−i−iii−i−ii
χ5733-3-3-33-13-131-31-31-3-133030-3-300-3-3003300-1-1111-1-1-10011001100-1-1000000000000000000i−i−ii−iii−ii−i−ii−iii−i
χ5833-3-3-33-13-131-31-31-3-133030-3-300-3-3003300-1-1111-1-1-10011001100-1-1000000000000000000−iii−ii−i−ii−iii−ii−i−ii
χ596666666-26-26-26-26-26-20-30-300-3-300-3-300-3-3-2-2-2-2-2-2001100110011001100000000000000000000000000000000
χ60666666-26-26-26-26-26-26-30-30-3-300-3-300-3-300-2-2-2-2-2-2110011001100110000000000000000000000000000000000
χ616666-6-66-26-26-26-2-62-620-30-300-3-300330033-2-2-2-2220011001100-1-100-1-100000000000000000000000000000000
χ626666-6-6-26-26-26-262-62-6-30-30-3-30033003300-2-2-2-22211001100-1-100-1-10000000000000000000000000000000000
χ6366-6-66-66-26-2-62-626-2-620-30-3003300-3-30033-2-222-22001100-1-1001100-1-100000000000000000000000000000000
χ6466-6-66-6-26-262-62-6-262-6-30-303300-3-3003300-2-222-221100-1-1001100-1-10000000000000000000000000000000000
χ6566-6-6-666-26-2-62-62-626-20-30-30033003300-3-3-2-2222-2001100-1-100-1-1001100000000000000000000000000000000
χ6666-6-6-66-26-262-62-62-6-26-30-3033003300-3-300-2-2222-21100-1-100-1-100110000000000000000000000000000000000
χ676-66-6006-2-626-2-620000060-6006-600000000-22-220000-2200-220000000000000000000000000000000000000000
χ686-66-6006-2-626-2-6200000-30300-3300−3i33i300−3i33i3-22-2200001-1001-100i3−i300i3−i300000000000000000000000000000000
χ696-66-6006-2-626-2-6200000-30300-33003i3−3i3003i3−3i3-22-2200001-1001-100−i3i300−i3i300000000000000000000000000000000
χ706-66-600-262-6-262-6000060-606-60000000000-22-2200-2200-22000000000000000000000000000000000000000000
χ716-66-600-262-6-262-60000-3030-3300−3i33i300−3i33i300-22-22001-1001-100i3−i300i3−i30000000000000000000000000000000000
χ726-66-600-262-6-262-60000-3030-33003i3−3i3003i3−3i300-22-22001-1001-100−i3i300−i3i30000000000000000000000000000000000
χ736-6-66006-2-62-626-20000060-600-6600000000-222-20000-22002-20000000000000000000000000000000000000000
χ746-6-66006-2-62-626-200000-303003-300−3i33i3003i3−3i3-222-200001-100-1100i3−i300−i3i300000000000000000000000000000000
χ756-6-66006-2-62-626-200000-303003-3003i3−3i300−3i33i3-222-200001-100-1100−i3i300i3−i300000000000000000000000000000000
χ766-6-6600-262-62-6-26000060-60-660000000000-222-200-22002-2000000000000000000000000000000000000000000
χ776-6-6600-262-62-6-260000-30303-300−3i33i3003i3−3i300-222-2001-100-1100i3−i300−i3i30000000000000000000000000000000000
χ786-6-6600-262-62-6-260000-30303-3003i3−3i300−3i33i300-222-2001-100-1100−i3i300i3−i30000000000000000000000000000000000
χ79999999-3-3-3-3-3-3-3-3-3-3-3-30000000000000000111111000000000000000000000000000000001111-1-1-1-1-1-1-1-11111
χ80999999-3-3-3-3-3-3-3-3-3-3-3-3000000000000000011111100000000000000000000000000000000-1-1-1-111111111-1-1-1-1
χ819999-9-9-3-3-3-3-3-3-3-3333300000000000000001111-1-10000000000000000000000000000000011-1-1-1-1-1-1111111-1-1
χ829999-9-9-3-3-3-3-3-3-3-3333300000000000000001111-1-100000000000000000000000000000000-1-1111111-1-1-1-1-1-111
χ8399-9-99-9-3-3-3-33333-3-333000000000000000011-1-11-100000000000000000000000000000000i−ii−i−i−iii−i−iiii−ii−i
χ8499-9-99-9-3-3-3-33333-3-333000000000000000011-1-11-100000000000000000000000000000000−ii−iiii−i−iii−i−i−ii−ii
χ8599-9-9-99-3-3-3-3333333-3-3000000000000000011-1-1-1100000000000000000000000000000000i−i−ii−i−iiiii−i−ii−i−ii
χ8699-9-9-99-3-3-3-3333333-3-3000000000000000011-1-1-1100000000000000000000000000000000−iii−iii−i−i−i−iii−iii−i
χ8718-1818-1800-6-666-6-666000000000000000000002-22-200000000000000000000000000000000000000000000000000
χ8818-18-181800-6-66666-6-6000000000000000000002-2-2200000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).