C₂₃×#2121 #15669740

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

Aliases

direct product

C₂₃×#2121

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#99
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×D₄	C₂³×C₂₃
prime radical	C₂₃×#534	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂³×C₂₃ ◁ C₂²×D₄×C₂₃ ◁ G

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

normal subgroups only

This group has 280 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)(26,32)(27,35,36,30)(28,31)(29,34,37,39)(33,38);(24,26)(25,29)(27,34)(28,33)(30,32)(31,37)(35,38)(36,39);(26,33)(29,37)(32,38)(34,39)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12705, C₂₃×#12706, C₂₃×#12725, …
maximal normal subgroup of	C₂₃×#12705, C₂₃×#12706, C₂₃×#12725, …
maximal quotient of	C₂₃×#11426, C₂₃×#11453, C₂₃×#11473, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 853);