C₃₁×#2248 #16842181

order	3968
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₁×#2248

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₁
prime radical	C₃₁×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(37,41)(38,45)(39,46)(42,47)(43,51)(44,50)(48,49);(36,37,42,51,39,43,38,41,40,44,45,49,46,48,47,50);(32,33,34,35)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#12318, C₃₁×#12319, C₃₁×#12320, …
maximal normal subgroup of	C₃₁×#12318, C₃₁×#12319, C₃₁×#12320, …
maximal quotient of	C₃₁×#12505, C₃₁×#12509, C₃₁×#12510, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 980);

C31×#2248 #16842181