C₂₃×#2551 #15670170

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#2551

Subgroups

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

556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 39
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26)(32,33,36,39)(34,38,35,37);(24,25,27,26)(28,29,30,31)(32,34,36,35)(33,37,39,38);(28,29)(30,31)(32,34,36,35)(33,37,39,38);(24,26,27,25)(32,35,36,34)(33,38,39,37)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10348, C₂₃×#10349, C₂₃×#10350, …
maximal normal subgroup of	C₂₃×#10348, C₂₃×#10349, C₂₃×#10350, …
maximal quotient of	C₂₃×#13910, C₂₃×#14005, C₂₃×#14053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1283);