C₂₃×#1890 #15669509

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#1890

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂⁴×C₂₃ ◁ G

386 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 736

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12754, C₂₃×#12760, C₂₃×#12761, …
maximal normal subgroup of	C₂₃×#12754, C₂₃×#12760, C₂₃×#12761, …
maximal quotient of	C₂₃×#8966, C₂₃×#8968, C₂₃×#9011, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 622);