C₂₃×#2005 #15669624

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2005

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

362 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 92 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)(30,38)(31,35)(32,41)(33,37)(34,39)(36,42)(40,43);(28,30,33,31)(29,34,37,43)(32,40,42,39)(35,41,38,36);(25,27)(28,31,33,30)(29,35,37,38)(32,39,42,40)(34,36,43,41)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2005, C₂₃×#23399, C₂₃×#23401, …
maximal normal subgroup of	C₂×C₂₃×#2005, C₂₃×#23399, C₂₃×#23401, …
maximal quotient of	C₂₃×#9917, C₂₃×#9919, C₂₃×#9925, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 737);