#1287×C₁₅₇ #34095645

order	20096
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₅₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

#1287×C₁₅₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₅₇	#95
commutator	C₂×C₄	C₄²×C₁₅₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₅₇
prime radical	C₂³×C₁₅₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₇ ◁ C₂×C₄²×C₁₅₇ ◁ G

126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 189
transitive degree	μ_t(G) = 10048

A minimal faithful permutation representation — 2 generators on 189 points:

(1,2,4,9,6,8,5,10)(3,11,12,16,13,7,14,15)(17,18)(19,25,27,31)(20,23)(21,24)(22,26,29,32)(28,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189);(1,3,5,12,6,13,4,14)(2,7,10,15,8,11,9,16)(17,19)(18,22,24,29)(20,26)(21,27)(23,25,30,31)(28,32)

Conjugacy classes & character table

5024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20096, 19);