Finite Group Databasebeta

← Group #10780607

Character table — Group #10780607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222224444444444444444444446666888888888888812121212121212121212121212121616161616161624243232484848
order12223444466622444888888881212121224242424224466881212122424242424244444448888888844824242424881212448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111
χ511111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1111-11-1-1
χ611111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-111-1-1-11-111
χ711111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-11-1-111
χ811111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-11111-111-1-1
χ9111111111111-1-11-1-11111-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111111-1-1-1-11
χ10111111111111-1-11-1-11111-1-1-1-1111111111111-1-1-1-11-1-111-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1-11111-1
χ11111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1-111-111-1-1-1-1-11111-1-111111-1-1-1-111-1
χ12111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-111-1-1-1-1-1111111-1-1-1-1-11111-1-11
χ13111111111111-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-11111-1-11-1-11-1-1-1-11111-11-111-1-111-11-11-1
χ14111111111111-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-11-1-11-1-1-1-111111-11-1-111-1-11-11-11
χ15111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-111-11111-1-1-1-1-11-111-1-1-1-1-111-11
χ16111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-111-11111-1-1-1-11-11-1-111111-1-11-1
χ17222222-2-2222222-2-2-2000000002-2-22000022222200-2-2-200000022-2-2-2-20000000000000000000000
χ18222222-2-2222222-2-2-2000000002-2-220000-2-2-2-22200-2-2-2000000-2-222220000000000000000000000
χ19222222-2-22222-2-2-222000000002-2-2200002222-2-200-222000000-2-2-222-20000000000000000000000
χ20222222-2-22222-2-2-222000000002-2-220000-2-2-2-2-2-200-222000000222-2-220000000000000000000000
χ2122222-222-222200-20022-2-20000-222-2-2-2-2-222-2-20000-20022000000-2002-2-222000000000000000000
χ2222222-222-222200-20022-2-20000-222-2-2-2-2-2-2-2220000-20022000000200-222-2-2000000000000000000
χ2322222-222-222200-200-2-2220000-222-2222222-2-20000-200-2-2000000-200222-2-2000000000000000000
χ2422222-222-222200-200-2-2220000-222-22222-2-2220000-200-2-2000000200-2-2-222000000000000000000
χ2522222-2-2-2-22220020000002i2i−2i−2i-2-2-2-2000022-2-20000200002i2i−2i−2i00200-200002i2i−2i−2i00000000000000
χ2622222-2-2-2-22220020000002i2i−2i−2i-2-2-2-20000-2-2220000200002i2i−2i−2i00-20020000−2i−2i2i2i00000000000000
χ2722222-2-2-2-2222002000000−2i−2i2i2i-2-2-2-2000022-2-2000020000−2i−2i2i2i00200-20000−2i−2i2i2i00000000000000
χ2822222-2-2-2-2222002000000−2i−2i2i2i-2-2-2-20000-2-222000020000−2i−2i2i2i00-200200002i2i−2i−2i00000000000000
χ292222-12222-1-1-12222222222222-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-1-1-1-100000000000000222-1-1-1-100-1-1000
χ302222-12222-1-1-12222222222222-1-1-1-1-1-1-1-10000-1-1-2-2-1-1-1-1-1-1-1-1-100000000000000-2-2-211110011000
χ312222-12222-1-1-122222-2-2-2-2-2-2-2-2-1-1-1-111110000-1-122-1-1-1111111000000000000002-2-2-1-11100-11000
χ322222-12222-1-1-122222-2-2-2-2-2-2-2-2-1-1-1-111110000-1-1-2-2-1-1-111111100000000000000-22211-1-1001-1000
χ332222-12222-1-1-1-2-22-2-22222-2-2-2-2-1-1-1-1-1-1-1-100001122-111-1-1111100000000000000-2-22-1-1-1-10011000
χ342222-12222-1-1-1-2-22-2-22222-2-2-2-2-1-1-1-1-1-1-1-1000011-2-2-111-1-111110000000000000022-2111100-1-1000
χ352222-12222-1-1-1-2-22-2-2-2-2-2-22222-1-1-1-1111100001122-11111-1-1-1-100000000000000-22-2-1-111001-1000
χ362222-12222-1-1-1-2-22-2-2-2-2-2-22222-1-1-1-11111000011-2-2-11111-1-1-1-1000000000000002-2211-1-100-11000
χ3722-2-22200-22-2-22-20002−22−22−22−2200-222−2−22-22-22-2000002−22−22−22-200002−22−22−22−200000000000000
χ3822-2-22200-22-2-22-20002−22−22−22−2200-222−2−2-22-222-2000002−22−22−2-220000−22−22−22−2200000000000000
χ3922-2-22200-22-2-22-2000−22−22−22−22200-2−2−2222-22-22-200000−22−22−222-20000−22−22−22−2200000000000000
χ4022-2-22200-22-2-22-2000−22−22−22−22200-2−2−222-22-222-200000−22−22−22-2200002−22−22−22−200000000000000
χ4122-2-22200-22-2-2-220002−22−2−22−22200-222−2−22-22-2-22000002−2−22−22-2200002−22−2−22−2200000000000000
χ4222-2-22200-22-2-2-220002−22−2−22−22200-222−2−2-22-22-22000002−2−22−222-20000−22−222−22−200000000000000
χ4322-2-22200-22-2-2-22000−22−222−22−2200-2−2−2222-22-2-2200000−222−22−2-220000−22−222−22−200000000000000
χ4422-2-22200-22-2-2-22000−22−222−22−2200-2−2−222-22-22-2200000−222−22−22-200002−22−2−22−2200000000000000
χ4522-2-22-20022-2-20002i−2i2−2−22−i2i2i2−i2-2002−2−2222-2-22000002i−2i2−2−i2i2i2−i20002i−2i0−222−2−i2i2i2−i200000000000000
χ4622-2-22-20022-2-20002i−2i2−2−22−i2i2i2−i2-2002−2−222-222-2000002i−2i2−2−i2i2i2−i2000−2i2i02−2−22i2−i2−i2i200000000000000
χ4722-2-22-20022-2-20002i−2i−222−2i2−i2−i2i2-200222−2−22-2-22000002i−2i−22i2−i2−i2i20002i−2i02−2−22i2−i2−i2i200000000000000
χ4822-2-22-20022-2-20002i−2i−222−2i2−i2−i2i2-200222−2−2-222-2000002i−2i−22i2−i2−i2i2000−2i2i0−222−2−i2i2i2−i200000000000000
χ4922-2-22-20022-2-2000−2i2i2−2−22i2−i2−i2i2-2002−2−2222-2-2200000−2i2i2−2i2−i2−i2i2000−2i2i0−222−2i2−i2−i2i200000000000000
χ5022-2-22-20022-2-2000−2i2i2−2−22i2−i2−i2i2-2002−2−222-222-200000−2i2i2−2i2−i2−i2i20002i−2i02−2−22−i2i2i2−i200000000000000
χ5122-2-22-20022-2-2000−2i2i−222−2−i2i2i2−i2-200222−2−22-2-2200000−2i2i−22−i2i2i2−i2000−2i2i02−2−22−i2i2i2−i200000000000000
χ5222-2-22-20022-2-2000−2i2i−222−2−i2i2i2−i2-200222−2−2-222-200000−2i2i−22−i2i2i2−i20002i−2i0−222−2i2−i2−i2i200000000000000
χ534444-24-4-44-2-2-244-4-4-400000000-222-200000000-2-2002220000000000000000000000000000000000
χ544444-24-4-44-2-2-2-4-4-44400000000-222-20000000022002-2-20000000000000000000000000000000000
χ554444-2-444-4-2-2-200-40044-4-400002-2-22222200000000200-2-200000000000000000000000000000000
χ564444-2-444-4-2-2-200-400-4-44400002-2-22-2-2-2-2000000002002200000000000000000000000000000000
χ574444-2-4-4-4-4-2-2-20040000004i4i−4i−4i2222000000000000-20000−2i−2i2i2i0000000000000000000000000000
χ584444-2-4-4-4-4-2-2-2004000000−4i−4i4i4i2222000000000000-200002i2i−2i−2i0000000000000000000000000000
χ5944-4-4-2400-4-2224-400022−2222−2222−2222−22-2002−2−2220000-2200000−22−22−220000000000000000000000000000
χ6044-4-4-2400-4-2224-4000−2222−2222−2222−2222-200222−2−20000-22000002−22−22−20000000000000000000000000000
χ6144-4-4-2400-4-222-4400022−2222−22−2222−2222-2002−2−22200002-200000−222−22−20000000000000000000000000000
χ6244-4-4-2400-4-222-44000−2222−222222−2222−22-200222−2−200002-2000002−2−22−220000000000000000000000000000
χ6344-4-4-2-4004-2220004i−4i22−22−2222−2i22i22i2−2i2200-222−2−2000000000−2i2i−22i2−i2−i2i20000000000000000000000000000
χ6444-4-4-2-4004-2220004i−4i−222222−222i2−2i2−2i22i2200-2−2−222000000000−2i2i2−2−i2i2i2−i20000000000000000000000000000
χ6544-4-4-2-4004-222000−4i4i22−22−22222i2−2i2−2i22i2200-222−2−20000000002i−2i−22−i2i2i2−i20000000000000000000000000000
χ6644-4-4-2-4004-222000−4i4i−222222−22−2i22i22i2−2i2200-2−2−2220000000002i−2i2−2i2−i2−i2i20000000000000000000000000000
χ674-4-44404-40-4-44000000000000004-40000000000000000000000000000000000000000000−2i22i200000
χ684-4-44404-40-4-44000000000000004-400000000000000000000000000000000000000000002i2−2i200000
χ694-4-4440-440-4-4400000000000000-440000000000022−220000000000000000000000000022−22000000000
χ704-4-4440-440-4-4400000000000000-4400000000000−222200000000000000000000000000−2222000000000
χ714-4-44-20-44022-2000000000000002-20−2i32i3−2i32i300000022−2200000000000000000000000000−22i6−i60000000
χ724-4-44-20-44022-2000000000000002-20−2i32i3−2i32i3000000−2222000000000000000000000000002−2−i6i60000000
χ734-4-44-20-44022-2000000000000002-202i3−2i32i3−2i300000022−2200000000000000000000000000−22−i6i60000000
χ744-4-44-20-44022-2000000000000002-202i3−2i32i3−2i3000000−2222000000000000000000000000002−2i6−i60000000
χ758-88-880000-88-8000000000000000000000000000000000000000000000000000000000000000000
χ768-88-8-400004-44000000000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ778-88-8-400004-4400000000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000
χ788-8-88-408-8044-400000000000000-4400000000000000000000000000000000000000000000000000

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