C₃₁×#386 #14520567

order	1984
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#386

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂³
commutator	C₂²	C₂²×C₄×C₃₁
Frattini, cosocle	C₂³	C₂³×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

286 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 43
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 3 generators on 43 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)(36,37,38,39)(41,43);(36,37)(38,39)(40,41,42,43);(32,33)(34,35)(36,37)(38,39)

Conjugacy classes & character table

868 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16843829, #16845658, #16845991, …
maximal subgroup of	C₃₁×#1390, C₃₁×#1790, C₃₁×#1867, …
maximal normal subgroup of	C₃₁×#1390, C₃₁×#1790, C₃₁×#1867, …
maximal quotient of	C₃₁×C₂²⋊#95, C₃₁×#1436, C₃₁×#1437, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 67);