C₂₃×#3483 #15671102

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₃×#3483

Subgroups

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

1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 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) = 1472

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)(25,29)(30,31)(32,33)(34,37)(35,39)(36,38);(24,25,28,29)(26,30,27,31)(32,34,37,33)(35,39,36,38);(24,26,28,27)(25,30,29,31)(32,35,37,36)(33,38,34,39);(24,26,28,27)(25,31,29,30)(32,36,37,35)(33,38,34,39);(24,27,28,26)(25,31,29,30)

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8441, C₂₃×#12773, C₂₃×#17520, …
maximal normal subgroup of	C₂₃×#8441, C₂₃×#12773, C₂₃×#17520, …
maximal quotient of	C₂₃×#34129, C₂₃×#34155, C₄×C₂₃×#550, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2215);