Finite Group Databasebeta

← Group #10695760

Character table — Group #10695760

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order122222222222366666664444666612121212444488881212121212121212121224242424242424242466121244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ922222222222222222222-2-2-2-22222-2-2-2-200000000-2-2000000000000000000000022-2-20000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-200000000-2-20000000000000000000000-2-2220000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-200000000000000000000000000000000002-2
χ1622222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-20000000000000000000000000000000000-22
χ1722222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2000000002200000000000000002-222-2-200000000000000
χ1822222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-200000000220000000000000000-22-2-22200000000000000
χ1922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-13333−3−3−3−33333−3−3−3−32-2-1-11100000000000000
χ2022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-13333−3−3−3−3−3−3−3−33333-2211-1-100000000000000
χ2122222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-1−3−3−3−333333333−3−3−3−3-2211-1-100000000000000
χ2222222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-1−3−3−3−33333−3−3−3−333332-2-1-11100000000000000
χ2322-222-2-2-22-2-22222-2-2-22-200002-2-220000000022−2−2000000000022−2−222−2−2000000002i−2i0000−i2−i2i2i200
χ2422-222-2-2-22-2-22222-2-2-22-200002-2-220000000022−2−2000000000022−2−222−2−200000000−2i2i0000i2i2−i2−i200
χ2522-222-2-2-22-2-22222-2-2-22-200002-2-2200000000−2−2220000000000−2−222−2−222000000002i−2i0000i2i2−i2−i200
χ2622-222-2-2-22-2-22222-2-2-22-200002-2-2200000000−2−2220000000000−2−222−2−22200000000−2i2i0000−i2−i2i2i200
χ272-222-22-2-2-22-222-2-222-22-20000-22-22000000002−22−200000000002−22−22−22−20000002i−2i000000−i2i2−i2i200
χ282-222-22-2-2-22-222-2-222-22-20000-22-22000000002−22−200000000002−22−22−22−2000000−2i2i000000i2−i2i2−i200
χ292-222-22-2-2-22-222-2-222-22-20000-22-2200000000−22−220000000000−22−22−22−220000002i−2i000000i2−i2i2−i200
χ302-222-22-2-2-22-222-2-222-22-20000-22-2200000000−22−220000000000−22−22−22−22000000−2i2i000000−i2i2−i2i200
χ312-2-22-2-22222-2-22-2-2-2-222222-2-222-2-222-2-22i2i−2i−2i00002-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ322-2-22-2-22222-2-22-2-2-2-222222-2-222-2-222-2-2−2i−2i2i2i00002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ332-2-22-2-22222-2-22-2-2-2-2222-2-22222-2-2-2-22200000000-220000000000000000000000000022-2-2000000
χ342-2-22-2-22222-2-22-2-2-2-2222-2-22222-2-2-2-22200000000-2200000000000000000000000000-2-222000000
χ352-2-22-2-22222-2-2-11111-1-1-122-2-2-1-111-1-1112i2i−2i−2i0000-11−i−iii−i−iii3−3−33−333−300−i3i3−i3i300000000000000
χ362-2-22-2-22222-2-2-11111-1-1-122-2-2-1-111-1-1112i2i−2i−2i0000-11−i−iii−i−iii−333−33−3−3300i3−i3i3−i300000000000000
χ372-2-22-2-22222-2-2-11111-1-1-122-2-2-1-111-1-111−2i−2i2i2i0000-11ii−i−iii−i−i3−3−33−333−300i3−i3i3−i300000000000000
χ382-2-22-2-22222-2-2-11111-1-1-122-2-2-1-111-1-111−2i−2i2i2i0000-11ii−i−iii−i−i−333−33−3−3300−i3i3−i3i300000000000000
χ392-2-22-2-222-2-2222-2-2-2-22222-2-22-2-22222-2-200000000-220000000000000000000000000000002-2-2200
χ402-2-22-2-222-2-2222-2-2-2-22222-2-22-2-22222-2-200000000-22000000000000000000000000000000-222-200
χ412-2-22-2-222-2-2222-2-2-2-2222-222-2-2-222-2-22200002-2-222-2000000002-2-222-2-2200000000000000000000
χ422-2-22-2-222-2-2222-2-2-2-2222-222-2-2-222-2-2220000-222-22-200000000-222-2-222-200000000000000000000
χ432-2-22-2-222-2-222-11111-1-1-1-222-211-1-111-1-100002-2-22-11−i3−i3i3i3i3i3−i3−i3-111-1-111-100−i3i3i3−i300000000000000
χ442-2-22-2-222-2-222-11111-1-1-1-222-211-1-111-1-100002-2-22-11i3i3−i3−i3−i3−i3i3i3-111-1-111-100i3−i3−i3i300000000000000
χ452-2-22-2-222-2-222-11111-1-1-1-222-211-1-111-1-10000-222-2-11−i3−i3i3i3i3i3−i3−i31-1-111-1-1100i3−i3−i3i300000000000000
χ462-2-22-2-222-2-222-11111-1-1-1-222-211-1-111-1-10000-222-2-11i3i3−i3−i3−i3−i3i3i31-1-111-1-1100−i3i3i3−i300000000000000
χ47444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2-2-2-2-24-44-42222-2-2-2-20000000022000000000000000000000000000000000000
χ49444-4-4-4-44000044-44-44-4-40000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ50444-4-4-4-44000044-44-44-4-4000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ51444-4-4-4-440000-2-22-22-2220000000023−2323−232i−2i2i−2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000
χ52444-4-4-4-440000-2-22-22-2220000000023−2323−23−2i2i−2i2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000
χ53444-4-4-4-440000-2-22-22-22200000000−2323−23232i−2i2i−2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000
χ54444-4-4-4-440000-2-22-22-22200000000−2323−2323−2i2i−2i2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000
χ5544-444-4-4-44-4-44-2-2-2222-220000-222-2000000002222−22−220000000000−2−222−2−22200000000000000000000
χ5644-444-4-4-44-4-44-2-2-2222-220000-222-200000000−22−222222000000000022−2−222−2−200000000000000000000
χ5744-444-4-4-4-444-4444-4-4-44-40000-444-400000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-444-4-2-2-2222-2200002-2-22000000000000000000000066−6−6−6−66600000000000000000000
χ5944-444-4-4-4-444-4-2-2-2222-2200002-2-220000000000000000000000−6−66666−6−600000000000000000000
χ6044-4-4-444-4000044-4-44-4-440000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ6144-4-4-444-4000044-4-44-4-44000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ624-444-44-4-44-44-44-4-444-44-400004-44-400000000000000000000000000000000000000000000000000
χ634-444-44-4-44-44-4-222-2-22-220000-22-2200000000000000000000006−66−6−66−6600000000000000000000
χ644-444-44-4-44-44-4-222-2-22-220000-22-220000000000000000000000−66−666−66−600000000000000000000
χ654-444-44-4-4-44-44-222-2-22-2200002-22-20000000022−2222−220000000000−22−22−22−2200000000000000000000
χ664-444-44-4-4-44-44-222-2-22-2200002-22-200000000−2222−222200000000002−22−22−22−200000000000000000000
χ674-44-44-44-400004-444-4-4-440000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ684-44-44-44-400004-444-4-4-44000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ694-4-44-4-44444-4-4-22222-2-2-2-4-444-2-22222-2-2000000002-2000000000000000000000000000000000000
χ704-4-44-4-444-4-444-22222-2-2-24-4-4422-2-2-2-222000000002-2000000000000000000000000000000000000
χ714-4-4-444-4400004-44-444-4-40000000000002-2-220000002-2-222-2-220000000000000000000000000000
χ724-4-4-444-4400004-44-444-4-4000000000000-222-2000000-222-2-222-20000000000000000000000000000
χ734-4-4-444-440000-22-22-2-2220000000023−23−23232-2-22000000−1−31+31+3−1−3−1+31−31−3−1+30000000000000000000000000000
χ744-4-4-444-440000-22-22-2-2220000000023−23−2323-222-20000001+3−1−3−1−31+31−3−1+3−1+31−30000000000000000000000000000
χ754-4-4-444-440000-22-22-2-22200000000−232323−232-2-22000000−1+31−31−3−1+3−1−31+31+3−1−30000000000000000000000000000
χ764-4-4-444-440000-22-22-2-22200000000−232323−23-222-20000001−3−1+3−1+31−31+3−1−3−1−31+30000000000000000000000000000
χ7788-8-8-888-80000-4-444-444-40000000000000000000000000000000000000000000000000000000000
χ788-88-88-88-80000-44-4-4444-40000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.