C₂₃×#2006 #15669625

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2006

Subgroups

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

406 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 35
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(29,33)(30,31)(34,35);(24,25)(26,27)(28,29)(30,35)(31,33)(32,34);(25,27)(28,29)(30,33)(31,35)(32,34)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7408, C₂₃×#12096, C₂₃×#12097, …
maximal normal subgroup of	C₂₃×#7408, C₂₃×#12096, C₂₃×#12097, …
maximal quotient of	C₂₃×#9930, C₂₃×#9931, C₂₃×#9932, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 738);