C₂₃×#1645 #15669264

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1645

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

200 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 47
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,28)(26,30)(29,31)(32,33,36,39)(34,40,41,47)(35,43,44,38)(37,45,46,42);(24,25,27,29)(26,31,30,28)(35,44)(38,43)(40,47)(42,45);(32,34,36,41)(33,37,39,46)(35,45,44,42)(38,47,43,40)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1645, C₂₃×#18515, C₂₃×#18518, …
maximal normal subgroup of	C₂×C₂₃×#1645, C₂₃×#18515, C₂₃×#18518, …
maximal quotient of	C₂₃×#7759, C₂₃×#7761, C₂₃×#7766, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 377);