C₃₁×#2435 #16842368

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₃₁×#2435

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂³×D₄×C₃₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

1088 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 4 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)(37,39)(41,44)(42,46);(33,35)(37,39)(40,41,43,44)(42,45,46,47);(32,33)(34,35)(36,37,38,39)(40,41)(42,45)(43,44)(46,47);(40,42,43,46)(41,45,44,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9459, C₃₁×#9947, C₃₁×#9955, …
maximal normal subgroup of	C₃₁×#9459, C₃₁×#9947, C₃₁×#9955, …
maximal quotient of	C₃₁×#13881, C₃₁×#13902, C₃₁×#13971, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1167);