C₃₁×#2583 #16842516

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₁×#2583

Subgroups

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

544 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)(32,33,34,35)(36,37)(38,39)(40,41)(42,43)(45,48)(46,50);(37,41)(38,42)(44,45,47,48)(46,49,50,51);(32,33)(34,35)(36,38,40,42)(37,39,41,43);(36,39)(37,42)(38,41)(40,43)(44,46)(45,49)(47,50)(48,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9408, C₃₁×#9412, C₃₁×#9943, …
maximal normal subgroup of	C₃₁×#9408, C₃₁×#9412, C₃₁×#9943, …
maximal quotient of	C₃₁×#13923, C₃₁×#13965, C₃₁×#14043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1315);

C31×#2583 #16842516