C₂₃×#1891 #15669510

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#1891

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#120
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#386
prime radical	C₂₃×#525	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

342 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 108 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)(24,25,28,32,29,26,30,34)(27,33,36,39,35,31,37,38);(24,26,28,34,29,25,30,32)(27,33,37,38,35,31,36,39);(24,27)(25,31)(26,33)(28,37)(29,35)(30,36)(32,39)(34,38)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12755, C₂₃×#12756, C₂₃×#12757, …
maximal normal subgroup of	C₂₃×#12755, C₂₃×#12756, C₂₃×#12757, …
maximal quotient of	C₂₃×#8965, C₂₃×#8966, C₂₃×#8967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 623);