C₂₃×#1868 #15669487

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

Aliases

direct product

C₂₃×#1868

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#120
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#385
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

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

normal subgroups only

This group has 260 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) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,32,29,33,39,45)(26,30,36,42,35,41,49,53)(27,31,38,44,37,43,50,54)(34,46,48,55,47,40,51,52);(24,26,28,36,29,35,39,49)(25,30,32,42,33,41,45,53)(27,34,38,48,37,47,50,51)(31,40,44,52,43,46,54,55);(24,27)(25,31)(26,34)(28,38)(29,37)(30,40)(32,44)(33,43)(35,47)(36,48)(39,50)(41,46)(42,52)(45,54)(49,51)(53,55)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12962, C₂₃×#12963, C₂₃×#12968, …
maximal normal subgroup of	C₂₃×#12962, C₂₃×#12963, C₂₃×#12968, …
maximal quotient of	C₂₃×#8851, C₂₃×#8852, C₂₃×#8861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 600);