C₂₃×#3549 #15671168

order	2944
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

C₂₃×#3549

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 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 — 5 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)(29,30)(33,36)(34,35);(24,25,28,27)(26,30,31,29)(32,33,37,36)(34,39,35,38);(32,34,37,35)(33,38,36,39);(24,26,28,31)(25,29,27,30)(32,35,37,34)(33,39,36,38);(24,27,28,25)(26,30,31,29)(32,36,37,33)(34,39,35,38)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8491, C₂₃×#8530, C₂₃×#12769, …
maximal normal subgroup of	C₂₃×#8491, C₂₃×#8530, C₂₃×#12769, …
maximal quotient of	C₂₃×#34368, C₂₃×#34415, C₂₃×#34485, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2281);