C₂₃×#3080 #15670699

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#3080

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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)(24,25,27,29)(26,30,31,28)(32,33,36,38)(34,42,44,47)(35,41,37,40)(39,45,46,43);(24,26,27,31)(25,28,29,30)(33,38)(39,46)(40,41)(42,47);(32,34)(33,39)(35,43)(36,44)(37,45)(38,46)(40,42)(41,47);(32,35,36,37)(33,40,38,41)(34,43,44,45)(39,42,46,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9351, C₂₃×#9352, C₂₃×#24724, …
maximal normal subgroup of	C₂₃×#9351, C₂₃×#9352, C₂₃×#24724, …
maximal quotient of	C₂₃×#20649, C₂₃×#20875, C₂₃×#21034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1812);