C₂₃×#2175 #15669794

order	2944
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2175

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator	C₈	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂×D₈×C₂₃	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

160 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 80 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 — 3 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)(24,25,27,26)(28,29)(30,33)(31,40)(32,34)(35,37)(36,38)(39,41)(42,43);(29,33)(30,37)(31,38)(34,41)(35,36)(39,43)(40,42);(24,26,27,25)(29,34)(33,41)(35,42)(36,40)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12065, C₂₃×#12077, C₂₃×#12080, …
maximal normal subgroup of	C₂₃×#12065, C₂₃×#12077, C₂₃×#12080, …
maximal quotient of	C₂₃×#12043, C₂₃×#12074, C₂₃×#12075, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 907);