C₂₃×#2843 #15670462

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2843

Subgroups

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

348 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 2944

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)(24,25,27,29)(26,28,30,31)(32,33)(34,38)(35,39)(36,37);(26,30)(28,31)(33,37)(35,38)(40,41,43,45)(42,46,47,44);(24,25)(26,28)(27,29)(30,31)(32,34)(33,38)(35,37)(36,39)(40,42,43,47)(41,44,45,46);(24,26)(25,28)(27,30)(29,31)(32,35,36,38)(33,39,37,34)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12183, C₂₃×#12259, C₂×C₂₃×#2843, …
maximal normal subgroup of	C₂₃×#12183, C₂₃×#12259, C₂×C₂₃×#2843, …
maximal quotient of	C₂₃×#14638, C₂₃×#14639, C₂₃×#14640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1575);