C₂₃×#1661 #15669280

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1661

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂₃×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 1472

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)(32,33,37,41)(34,42,44,47)(35,40,36,39)(38,45,46,43);(26,30)(28,31)(32,34)(33,38)(35,45)(36,43)(37,44)(39,47)(40,42)(41,46);(24,25,27,29)(26,31,30,28)(32,34)(33,38)(35,43)(36,45)(37,44)(39,42)(40,47)(41,46)

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1661, C₂₃×#18984, C₂₃×#18987, …
maximal normal subgroup of	C₂×C₂₃×#1661, C₂₃×#18984, C₂₃×#18987, …
maximal quotient of	C₂₃×#7752, C₂₃×#7753, C₂₃×#7756, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 393);