C₂₃×#2644 #15670263

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2644

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

420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 1472

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)(25,28)(29,30)(32,33)(34,37)(35,38)(36,39)(40,41,44,46)(42,47,43,45);(24,25,27,28)(26,29,31,30)(32,34)(33,35)(36,38)(37,39)(40,42,44,43)(41,45,46,47);(24,25)(26,30)(27,28)(29,31)(32,34)(33,37)(35,39)(36,38)(40,41)(42,45)(43,47)(44,46);(24,26,27,31)(25,29,28,30)(32,35,36,37)(33,38,39,34)(40,43,44,42)(41,45,46,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#29436, C₂₃×#29437, C₂₃×#29442, …
maximal normal subgroup of	C₂₃×#29436, C₂₃×#29437, C₂₃×#29442, …
maximal quotient of	C₂₃×#14260, C₂₃×#14266, C₂₃×#14331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1376);