C₃₁×#1949 #16841882

order	3968
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₁×#1949

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(40,41)(42,44)(43,45)(46,47);(36,38,39,37)(41,44)(42,47)(45,46);(32,33,34,35)(41,45)(44,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₁×#1949, C₃₁×#21169, C₃₁×#21170, …
maximal normal subgroup of	C₂×C₃₁×#1949, C₃₁×#21169, C₃₁×#21170, …
maximal quotient of	C₃₁×#9603, C₃₁×#9606, C₃₁×#9613, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 681);

C31×#1949 #16841882