C₂₃×#2502 #15670121

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#2502

Subgroups

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

544 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 43
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 43 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)(28,29)(30,34)(31,33)(32,35)(36,37,40,43)(38,42,39,41);(28,29,31,33)(30,32,35,34)(36,38,40,39)(37,41,43,42);(24,25,26,27)(28,29)(30,32)(31,33)(34,35);(28,30,31,35)(29,32,33,34)(36,39,40,38)(37,42,43,41)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9461, C₂₃×#9951, C₂₃×#9959, …
maximal normal subgroup of	C₂₃×#9461, C₂₃×#9951, C₂₃×#9959, …
maximal quotient of	C₂₃×#13880, C₂₃×#13924, C₂₃×#14000, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1234);