C₃₁×#3515 #16843448

order	3968
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₁×#3515

Subgroups

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

1014 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)(37,39)(40,41,45,46)(42,43,47,50)(44,52,53,48)(49,55,54,51);(41,46)(43,50)(48,52)(51,55);(32,33)(34,37)(35,36)(38,39)(40,42,45,47)(41,43,46,50)(44,49,53,54)(48,51,52,55);(40,43)(41,47)(42,46)(44,51)(45,50)(48,54)(49,52)(53,55);(32,34,35,38)(33,37,36,39)(40,44)(41,48)(42,49)(43,51)(45,53)(46,52)(47,54)(50,55)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8415, C₃₁×#17653, C₃₁×#17680, …
maximal normal subgroup of	C₃₁×#8415, C₃₁×#17653, C₃₁×#17680, …
maximal quotient of	C₃₁×#34191, C₃₁×#34229, C₃₁×#34231, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2247);

C31×#3515 #16843448