C₂₃×#2785 #15670404

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₂₃×#2785

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

428 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 176 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)(24,25,28,26)(27,30,31,29)(32,33)(34,37)(35,36)(38,39)(41,42)(45,46);(25,26)(27,31)(33,35)(37,38)(40,41,44,42)(43,46,47,45);(24,26,28,25)(27,30,31,29)(32,34,36,39)(33,37,35,38)(40,42,44,41)(43,46,47,45);(24,27,28,31)(25,29,26,30)(32,35,36,33)(34,38,39,37)(40,43)(41,45)(42,46)(44,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12145, C₂₃×#12239, C₂₃×#36796, …
maximal normal subgroup of	C₂₃×#12145, C₂₃×#12239, C₂₃×#36796, …
maximal quotient of	C₂₃×#14399, C₂₃×#14476, C₂₃×#14589, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1517);