C₃₁×#525 #14520706

order	1984
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#525

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

330 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 170 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) = 496

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

Conjugacy classes & character table

868 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16844202, #16844215, #16844254, …
maximal subgroup of	C₃₁×#1501, C₃₁×#1504, C₃₁×#1513, …
maximal normal subgroup of	C₃₁×#1501, C₃₁×#1504, C₃₁×#1513, …
maximal quotient of	C₃₁×#2280, C₃₁×#2290, C₃₁×#2296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 206);