C₂₃×#2309 #15669928

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

direct product

C₂₃×#2309

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

1104 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 360 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) = 736

A minimal faithful permutation representation — 4 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)(25,27)(28,29,30,31)(33,36)(34,38);(32,33,35,36)(34,37,38,39);(24,25)(26,27)(28,29)(30,31)(32,33)(34,37)(35,36)(38,39);(32,34)(33,37)(35,38)(36,39)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8748, C₂₃×#8749, C₂₃×#9497, …
maximal normal subgroup of	C₂₃×#8748, C₂₃×#8749, C₂₃×#9497, …
maximal quotient of	C₂₃×#13775, C₂₃×#13785, C₂₃×#13795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1041);