C₃₁×#2933 #16842866

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

Aliases

direct product

C₃₁×#2933

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂³×C₄
prime radical	C₃₁×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 4 generators on 51 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)(34,35)(36,37,39,42,40,43,46,49)(38,41,45,48,44,47,50,51);(33,35);(36,38,39,45,40,44,46,50)(37,41,42,48,43,47,49,51);(38,44)(41,47)(45,50)(48,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#22886, C₃₁×#22887, C₃₁×#22888, …
maximal normal subgroup of	C₃₁×#22886, C₃₁×#22887, C₃₁×#22888, …
maximal quotient of	C₃₁×#17994, C₃₁×#17995, C₃₁×#17996, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1665);

C31×#2933 #16842866