C₂₃×#2402 #15670021

order	2944
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2402

Subgroups

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

400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 2944

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10372, C₂₃×#10373, C₂₃×#21676, …
maximal normal subgroup of	C₂₃×#10372, C₂₃×#10373, C₂₃×#21676, …
maximal quotient of	C₂₃×#13846, C₂₃×#13848, C₂₃×#13854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1134);