C₂₃×#2242 #15669861

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₃×#2242

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂×D₈×C₂₃	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 63
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 63 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)(26,29)(27,28)(30,31)(32,33)(34,46)(35,40)(36,54)(37,57)(38,58)(39,45)(41,50)(42,47)(43,56)(44,55)(48,60)(49,59)(51,63)(52,62)(53,61);(25,28)(29,31)(32,34,47,52,38,49,56,53,39,50,37,48,55,51,36,35)(33,40,54,63,44,60,57,41,45,61,43,59,58,62,42,46);(24,26,27,30)(25,29,28,31)(32,35,36,51,55,48,37,50,39,53,56,49,38,52,47,34)(33,41,42,60,58,63,43,40,45,46,57,62,44,59,54,61)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2242, C₂₃×#33697, C₂₃×#33702, …
maximal normal subgroup of	C₂×C₂₃×#2242, C₂₃×#33697, C₂₃×#33702, …
maximal quotient of	C₂₃×#12889, C₂₃×#13147, C₂₃×#13148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 974);