C₂₃×#3138 #15670757

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#3138

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

484 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 192 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)(24,25)(26,29)(27,28)(30,31)(33,38)(34,39)(35,36);(25,28)(29,31)(32,33,36,34,37,39,35,38);(24,26,27,30)(25,29,28,31)(32,34,35,33,37,38,36,39);(33,39)(34,38)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9424, C₂₃×#9425, C₂₃×#9438, …
maximal normal subgroup of	C₂₃×#9424, C₂₃×#9425, C₂₃×#9438, …
maximal quotient of	C₂₃×#20764, C₂₃×#21095, C₂₃×#21203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1870);