C₃₁×#2153 #16842086

order	3968
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₁×#2153

Subgroups

	subgroup	G/H
center	C₈×C₃₁	C₂×D₄
commutator	C₄	C₂²×C₈×C₃₁
Frattini, cosocle	C₂×C₈	C₂³×C₃₁
socle	C₂×C₃₁	C₂×C₄⋊C₈
prime radical	C₂³×C₃₁	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₁ ◁ C₂²×C₈×C₃₁ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 3 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33,36,41,37,40,50,55,38,42,51,56,35,48,49,61)(34,43,46,58,47,53,60,62,44,57,59,63,45,39,52,54);(32,34,35,45,38,44,37,47)(33,39,40,43,42,53,48,57)(36,46,49,52,51,59,50,60)(41,54,55,58,56,62,61,63);(34,44)(39,53)(43,57)(45,47)(46,59)(52,60)(54,62)(58,63)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#11989, C₃₁×#11990, C₃₁×#11991, …
maximal normal subgroup of	C₃₁×#11989, C₃₁×#11990, C₃₁×#11991, …
maximal quotient of	C₃₁×#11997, C₃₁×#12005, C₃₁×#12014, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 885);

C31×#2153 #16842086