C₃₁×#2473 #16842406

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

Aliases

direct product

C₃₁×#2473

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

520 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)(36,37,40,38)(39,42,43,41)(44,45)(46,47)(48,50)(49,51);(33,35)(37,38)(41,42)(44,46,48,51)(45,47,50,49);(32,33)(34,35)(36,38,40,37)(39,42,43,41)(44,46)(45,49)(47,50)(48,51);(36,39)(37,41)(38,42)(40,43)(44,47,48,49)(45,46,50,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₁×#2473, C₃₁×#34670, C₃₁×#34691, …
maximal normal subgroup of	C₂×C₃₁×#2473, C₃₁×#34670, C₃₁×#34691, …
maximal quotient of	C₃₁×#13882, C₃₁×#13896, C₃₁×#13985, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1205);

C31×#2473 #16842406