C₂₃×#1820 #15669439

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#1820

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂⁴×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

300 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 736

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7214, C₂₃×#7348, C₂₃×#8463, …
maximal normal subgroup of	C₂₃×#7214, C₂₃×#7348, C₂₃×#8463, …
maximal quotient of	C₂₃×#8699, C₂₃×#8701, C₂₃×#8703, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 552);