C₂₃×#1718 #15669337

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₃×#1718

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

164 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 72 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)(26,32,33,39)(27,35,36,30)(29,37,38,34)(40,41)(42,48)(43,45)(44,52)(46,50)(47,51)(49,54)(53,55);(24,26,27,34,28,33,36,37)(25,29,30,32,31,38,35,39)(41,45)(46,53)(47,52)(48,54);(26,33)(29,38)(32,39)(34,37)(40,42,44,50,43,49,51,55)(41,46,47,48,45,53,52,54)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1718, C₂₃×#19613, C₂₃×#19620, …
maximal normal subgroup of	C₂×C₂₃×#1718, C₂₃×#19613, C₂₃×#19620, …
maximal quotient of	C₂₃×#8821, C₂₃×#9826, C₂₃×#9828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 450);