C₂₃×#1719 #15669338

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

Aliases

direct product

C₂₃×#1719

Subgroups

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

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

normal subgroups only

This group has 186 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1719, C₂₃×#19613, C₂₃×#19619, …
maximal normal subgroup of	C₂×C₂₃×#1719, C₂₃×#19613, C₂₃×#19619, …
maximal quotient of	C₂₃×#8821, C₂₃×#9826, C₂₃×#9829, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 451);