C₃₁×#3547 #16843480

order	3968
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₁×#3547

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 5 generators on 55 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)(33,36)(34,38)(40,41,44,45)(42,48,49,46)(43,51,52,47)(50,53,55,54);(33,36)(37,39)(41,45)(42,49)(47,51)(50,55);(32,33,35,36)(34,37,38,39)(40,42,44,49)(41,46,45,48)(43,50,52,55)(47,53,51,54);(32,34)(33,37)(35,38)(36,39)(40,41)(42,46)(43,47)(44,45)(48,49)(50,53)(51,52)(54,55);(40,43,44,52)(41,47,45,51)(42,50,49,55)(46,53,48,54)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8502, C₃₁×#18706, C₃₁×#18707, …
maximal normal subgroup of	C₃₁×#8502, C₃₁×#18706, C₃₁×#18707, …
maximal quotient of	C₃₁×#34367, C₃₁×#34383, C₃₁×#34394, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2279);

C31×#3547 #16843480