C₂₃×#1684 #15669303

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#1684

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

144 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 2944

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)(24,25,28,31)(26,32,35,39)(27,36,33,30)(29,37,38,34)(40,41)(42,48)(43,45)(44,52)(46,50)(47,51)(49,55)(53,54);(24,26,33,37,28,35,27,34)(25,29,36,39,31,38,30,32)(41,45)(46,54)(47,52)(48,55);(40,42,43,49)(41,46,45,54)(44,53,51,50)(47,55,52,48)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1684, C₂₃×#19123, C₂₃×#19126, …
maximal normal subgroup of	C₂×C₂₃×#1684, C₂₃×#19123, C₂₃×#19126, …
maximal quotient of	C₂₃×#8649, C₂₃×#9216, C₂₃×#9220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 416);