C₂₃×#1827 #15669446

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1827

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#117
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#381
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂₃×#117 ◁ G

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

normal subgroups only

This group has 262 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)(26,33,35,29)(27,32)(28,31)(30,34,37,39)(36,38);(24,26)(25,29)(27,34)(28,35)(30,32)(31,33)(36,39)(37,38);(24,26)(25,30,31,37)(27,34)(28,35)(29,32,33,38)(36,39)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12719, C₂₃×#12720, C₂₃×#12721, …
maximal normal subgroup of	C₂₃×#12719, C₂₃×#12720, C₂₃×#12721, …
maximal quotient of	C₂₃×#8730, C₂₃×#8731, C₂₃×#8732, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 559);