C₃₁×#2241 #16842174

order	3968
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃₁×#2241

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 3 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)(32,33)(34,37)(35,36)(38,39)(40,41,47,42)(43,44,53,55)(45,52,48,49)(46,54,51,50);(33,36)(37,39)(40,42,45,53,46,54,44,52,47,41,48,43,51,50,55,49);(32,34,35,38)(33,37,36,39)(40,43,44,42,51,52,45,50,47,53,55,41,46,49,48,54)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#12344, C₃₁×#12345, C₃₁×#12346, …
maximal normal subgroup of	C₃₁×#12344, C₃₁×#12345, C₃₁×#12346, …
maximal quotient of	C₃₁×#12888, C₃₁×#13148, C₃₁×#13203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 973);

C31×#2241 #16842174