C₂₃×#1819 #15669438

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×#1819

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂⁵×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂⁵×C₂₃ ◁ G

504 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 3 generators on 39 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)(26,32,34,30)(27,29)(28,31)(33,38,39,36)(35,37);(25,29)(30,36)(31,37)(32,38);(24,26,27,33)(25,30,29,36)(28,34,35,39)(31,32,37,38)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7213, C₂₃×#7349, C₂₃×#8535, …
maximal normal subgroup of	C₂₃×#7213, C₂₃×#7349, C₂₃×#8535, …
maximal quotient of	C₂₃×#8698, C₂₃×#8700, C₂₃×#8702, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 551);