C₂₃×#1613 #15669232

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1613

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#534	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 736

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

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12120, C₂₃×#12122, C₂₃×#12124, …
maximal normal subgroup of	C₂₃×#12120, C₂₃×#12122, C₂₃×#12124, …
maximal quotient of	C₂₃×#7786, C₂₃×#7800, C₂₃×#7801, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 345);