C₃₁×#2604 #16842537

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

Aliases

direct product

C₃₁×#2604

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

470 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)(33,35)(44,45,48,51)(46,50,47,49);(37,40)(41,43)(44,46,48,47)(45,49,51,50);(32,33,34,35)(36,37)(38,41)(39,40)(42,43)(44,47,48,46)(45,50,51,49);(36,38,39,42)(37,41,40,43)(44,45)(46,49)(47,50)(48,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#18281, C₃₁×#18283, C₂×C₃₁×#2604, …
maximal normal subgroup of	C₃₁×#18281, C₃₁×#18283, C₂×C₃₁×#2604, …
maximal quotient of	C₃₁×#13952, C₃₁×#13961, C₃₁×#14077, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1336);

C31×#2604 #16842537