C₂₃×#3058 #15670677

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#3058

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

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

normal subgroups only

This group has 524 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) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 43 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)(26,27)(29,33)(31,34)(35,39)(36,40)(38,41)(42,43);(28,29,34,40,32,36,31,33)(30,35,41,43,37,42,38,39);(25,27)(28,30)(29,35)(31,38)(32,37)(33,39)(34,41)(36,42)(40,43);(30,37)(35,42)(38,41)(39,43)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#11868, C₂₃×#11870, C₂₃×#13074, …
maximal normal subgroup of	C₂₃×#11868, C₂₃×#11870, C₂₃×#13074, …
maximal quotient of	C₂₃×#19187, C₂₃×#19192, C₂₃×#19198, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1790);