C₂₃×#2875 #15670494

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#2875

Subgroups

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

556 conjugacy classes of subgroups; only the 504 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 504 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) = 43
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(28,29,31,35,32,33,38,40)(30,34,37,41,36,39,42,43);(24,25,26,27)(29,33)(34,39)(35,40)(41,43);(28,30)(29,34)(31,37)(32,36)(33,39)(35,41)(38,42)(40,43);(30,36)(34,39)(37,42)(41,43)

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#9311, C₂₃×#9312, C₂₃×#12609, …
maximal normal subgroup of	C₂₃×#9311, C₂₃×#9312, C₂₃×#12609, …
maximal quotient of	C₂₃×#17316, C₂₃×#17320, C₂₃×#17329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1607);