C₂₃×#1509 #15669128

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

242 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 92 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 — 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)(25,28)(26,30)(29,31)(33,37,38,39);(24,25)(26,31)(27,29)(28,30)(32,33)(34,37)(35,39)(36,38);(25,29)(28,31)(32,34,36,35)(33,37,38,39)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8416, C₂₃×#8417, C₂₃×#8418, …
maximal normal subgroup of	C₂₃×#8416, C₂₃×#8417, C₂₃×#8418, …
maximal quotient of	C₂₃×#7574, C₂₃×#7577, C₂₃×#7584, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 241);