C₃₁×#2395 #16842328

order	3968
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₁×#2395

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂⁴
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1984

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9011, C₃₁×#9012, C₃₁×#11727, …
maximal normal subgroup of	C₃₁×#9011, C₃₁×#9012, C₃₁×#11727, …
maximal quotient of	C₃₁×#13839, C₃₁×#13842, C₃₁×#13844, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1127);

C31×#2395 #16842328