C₃₁×#2365 #16842298

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#2365

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁴×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 4 generators on 47 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)(33,35)(36,37,39,38)(41,44)(45,46);(36,38,39,37)(40,41)(42,46)(43,44)(45,47);(32,33,34,35);(40,42,43,47)(41,45,44,46)

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8922, C₃₁×#8923, C₃₁×#8925, …
maximal normal subgroup of	C₃₁×#8922, C₃₁×#8923, C₃₁×#8925, …
maximal quotient of	C₄⋊C₄²×C₃₁, C₃₁×#13817, C₃₁×#13821, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1097);

C31×#2365 #16842298