C₂₃×#3199 #15670818

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3198
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#3199

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

442 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 736

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12108, C₂₃×#12111, C₂₃×#12117, …
maximal normal subgroup of	C₂₃×#12108, C₂₃×#12111, C₂₃×#12117, …
maximal quotient of	C₂₃×#21770, C₂₃×#21947, C₂₃×#22056, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1931);