C₂₃×#2621 #15670240

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#2621

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

528 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(28,29,30,31)(33,37)(38,40)(39,45)(46,47);(25,27)(32,33)(34,40)(35,39)(36,37)(38,42)(41,47)(43,46)(44,45);(24,25)(26,27)(28,29)(30,31)(32,34,36,42)(33,38,37,40)(35,43,44,41)(39,47,45,46);(32,35,36,44)(33,39,37,45)(34,41,42,43)(38,46,40,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9195, C₂₃×#9196, C₂₃×#11694, …
maximal normal subgroup of	C₂₃×#9195, C₂₃×#9196, C₂₃×#11694, …
maximal quotient of	C₂₃×#14258, C₂₃×#14261, C₂₃×#14274, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1353);