C₂₃×#2022 #15669641

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2022

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂₃×#534	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂⁴×C₂₃ ◁ G

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

normal subgroups only

This group has 430 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)(30,33)(31,34)(32,35)(36,39)(37,40)(38,42)(41,43);(28,30,32,37)(29,33,35,40)(31,36,38,43)(34,41,42,39);(25,27)(28,31)(29,34)(30,36)(32,38)(33,39)(35,42)(37,43)(40,41)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7395, C₂₃×#12092, C₂₃×#12094, …
maximal normal subgroup of	C₂₃×#7395, C₂₃×#12092, C₂₃×#12094, …
maximal quotient of	C₂₃×#9918, C₂₃×#9919, C₂₃×#9920, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 754);