C₂₃×#2122 #15669741

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#2122

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#99
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×D₄	C₂³×C₂₃
prime radical	C₂₃×#535	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

266 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 3 generators on 39 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)(27,34,35,29)(28,31)(32,38)(33,37,39,36);(25,29)(26,32)(30,37)(31,34)(33,39)(36,38);(24,26,28,32)(25,30,31,38)(27,33,35,39)(29,36,34,37)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12715, C₂₃×#12718, C₂₃×#12721, …
maximal normal subgroup of	C₂₃×#12715, C₂₃×#12718, C₂₃×#12721, …
maximal quotient of	C₂₃×#11427, C₂₃×#11454, C₂₃×#11473, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 854);