C₂₃×#2683 #15670302

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#2683

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

592 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 1472

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)(24,25,26,27)(33,36)(37,38);(29,31)(32,33,35,36)(34,38,39,37);(24,25)(26,27)(28,29)(30,31)(32,33)(34,37)(35,36)(38,39);(24,25)(26,27)(32,34,35,39)(33,37,36,38)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7738, C₂₃×#7754, C₂₃×#7764, …
maximal normal subgroup of	C₂₃×#7738, C₂₃×#7754, C₂₃×#7764, …
maximal quotient of	C₂₃×#14362, C₂₃×#14401, C₂₃×#14440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1415);