C₂₃×#2046 #15669665

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2046

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

276 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 84 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)(24,25)(26,27)(28,29,32,36)(30,37,38,34)(31,33,40,35)(39,42,43,41);(29,33)(30,38)(31,40)(34,42)(35,36)(37,41);(25,27)(28,30,31,39,32,38,40,43)(29,34,35,42,36,37,33,41)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2046, C₂₃×#23520, C₂₃×#23521, …
maximal normal subgroup of	C₂×C₂₃×#2046, C₂₃×#23520, C₂₃×#23521, …
maximal quotient of	C₂₃×#10442, C₂₃×#10443, C₂₃×#10444, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 778);