C₂₃×#2607 #15670226

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#2607

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

444 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 200 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)(32,33)(34,38)(35,36)(37,39)(40,41,44,43)(42,46,47,45);(25,28)(29,31)(33,36)(37,38)(42,47)(45,46);(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39)(40,42,44,47)(41,45,43,46);(24,26,27,30)(25,29,28,31)(32,34)(33,37)(35,39)(36,38)(40,43,44,41)(42,46,47,45)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10386, C₂₃×#10387, C₂₃×#12121, …
maximal normal subgroup of	C₂₃×#10386, C₂₃×#10387, C₂₃×#12121, …
maximal quotient of	C₂₃×#13953, C₂₃×#14091, C₂₃×#14093, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1339);