C₃₁×#3532 #16843465

order	3968
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₁×#3532

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 496

A minimal faithful permutation representation — 5 generators on 47 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)(34,40)(35,39)(36,38)(37,42)(41,44)(43,46)(45,47);(32,34)(33,37)(35,42)(36,41)(38,45)(39,40)(43,47)(44,46);(33,38)(34,41)(39,46)(42,47);(33,38)(34,42)(37,44)(39,46)(40,45)(41,47);(33,39)(37,40)(38,46)(44,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#12753, C₃₁×#33551, C₂×C₃₁×#3532, …
maximal normal subgroup of	C₃₁×#12753, C₃₁×#33551, C₂×C₃₁×#3532, …
maximal quotient of	C₃₁×#34356, C₃₁×#34406, C₃₁×#34407, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2264);

C31×#3532 #16843465