Finite Group Databasebeta

← Group #72224461

Character table — Group #72224461

Order 15600.

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅
size	1	325	624	650	650	650	1200	1200	1200	1300	1300	1300	1300	1950	1950
order	1	2	5	3	4	6	13	13	13	4	12	12	12	8	8
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	1	1	1	1	1	1	1	1	-1	1	-1	-1	-1	-1
χ₃	25	1	0	1	1	1	-1	-1	-1	1	1	1	1	-1	-1
χ₄	25	1	0	1	1	1	-1	-1	-1	-1	1	-1	-1	1	1
χ₅	26	2	1	2	-2	2	0	0	0	0	-2	0	0	0	0
χ₆	26	2	1	-1	2	-1	0	0	0	2	-1	-1	-1	0	0
χ₇	26	2	1	-1	2	-1	0	0	0	-2	-1	1	1	0	0
χ₈	26	2	1	-1	-2	-1	0	0	0	0	1	$- i \sqrt{3}$	$i \sqrt{3}$	0	0
χ₉	26	2	1	-1	-2	-1	0	0	0	0	1	$i \sqrt{3}$	$- i \sqrt{3}$	0	0
χ₁₀	26	-2	1	2	0	-2	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$
χ₁₁	26	-2	1	2	0	-2	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$
χ₁₂	48	0	-2	0	0	0	−ζ⁴−ζ²⁰−ζ¹⁰⁰−ζ¹²⁴−ζ¹⁸⁸−ζ²¹²−ζ²⁹²−ζ³⁰⁸	−ζ²⁸−ζ⁶⁸−ζ⁷⁶−ζ¹⁴⁰−ζ¹⁷²−ζ²³⁶−ζ²⁴⁴−ζ²⁸⁴	−ζ⁴⁴−ζ⁹²−ζ¹¹⁶−ζ¹⁴⁸−ζ¹⁶⁴−ζ¹⁹⁶−ζ²²⁰−ζ²⁶⁸	0	0	0	0	0	0
χ₁₃	48	0	-2	0	0	0	−ζ²⁸−ζ⁶⁸−ζ⁷⁶−ζ¹⁴⁰−ζ¹⁷²−ζ²³⁶−ζ²⁴⁴−ζ²⁸⁴	−ζ⁴⁴−ζ⁹²−ζ¹¹⁶−ζ¹⁴⁸−ζ¹⁶⁴−ζ¹⁹⁶−ζ²²⁰−ζ²⁶⁸	−ζ⁴−ζ²⁰−ζ¹⁰⁰−ζ¹²⁴−ζ¹⁸⁸−ζ²¹²−ζ²⁹²−ζ³⁰⁸	0	0	0	0	0	0
χ₁₄	48	0	-2	0	0	0	−ζ⁴⁴−ζ⁹²−ζ¹¹⁶−ζ¹⁴⁸−ζ¹⁶⁴−ζ¹⁹⁶−ζ²²⁰−ζ²⁶⁸	−ζ⁴−ζ²⁰−ζ¹⁰⁰−ζ¹²⁴−ζ¹⁸⁸−ζ²¹²−ζ²⁹²−ζ³⁰⁸	−ζ²⁸−ζ⁶⁸−ζ⁷⁶−ζ¹⁴⁰−ζ¹⁷²−ζ²³⁶−ζ²⁴⁴−ζ²⁸⁴	0	0	0	0	0	0
χ₁₅	52	-4	2	-2	0	2	0	0	0	0	0	0	0	0	0

Here ζ is a primitive root of unity of order 312 (ζ³¹² = 1); i = ζ⁷⁸.