#102×C₁₅₁ #18012602

order	4832
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₅₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#102×C₁₅₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₅₁	D₄
commutator	C₄	C₂×C₄×C₁₅₁
Frattini, cosocle	C₂×C₄	C₂²×C₁₅₁
prime radical	C₂×D₄×C₁₅₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂×C₄×C₁₅₁ ◁ G

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 163
transitive degree	μ_t(G) = 2416

A minimal faithful permutation representation — 2 generators on 163 points:

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

Conjugacy classes & character table

2114 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#102×C₁₅₁, #416×C₁₅₁, #417×C₁₅₁, …
maximal normal subgroup of	C₂×#102×C₁₅₁, #416×C₁₅₁, #417×C₁₅₁, …
maximal quotient of	D₄⋊C₈×C₁₅₁, #327×C₁₅₁, #331×C₁₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4832, 9);

#102×C151 #18012602