C₂₃×#2616 #15670235

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#2616

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂²×#41×C₂₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

816 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 232 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 — 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)(29,31)(32,33)(34,36)(35,37)(38,39);(25,27)(29,31)(33,34)(37,38);(24,25)(26,27)(28,29)(30,31)(32,34,36,33)(35,37,39,38);(32,35,36,39)(33,37,34,38)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9931, C₂₃×#9935, C₂₃×#18230, …
maximal normal subgroup of	C₂₃×#9931, C₂₃×#9935, C₂₃×#18230, …
maximal quotient of	C₂₃×#14258, C₂₃×#14264, C₂₃×#14300, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1348);