C₂₃×#1828 #15669447

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1828

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#381
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂⁴×C₂₃ ◁ G

296 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 100 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)(26,32,34,29)(27,35)(28,31)(30,36)(33,37,39,38);(24,26)(25,29)(27,33)(28,34)(30,37)(31,32)(35,38)(36,39);(24,27)(25,30,31,35)(26,33)(28,36)(29,37,32,38)(34,39)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12725, C₂₃×#12726, C₂₃×#12727, …
maximal normal subgroup of	C₂₃×#12725, C₂₃×#12726, C₂₃×#12727, …
maximal quotient of	C₂₃×#8734, C₂₃×#8735, C₂₃×#8736, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 560);