C₂₃×#1698 #15669317

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#1698

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

156 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 64 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)(26,30)(29,31)(32,33)(34,40)(35,37)(36,44)(38,42)(39,43)(41,47)(45,46);(24,25,26,28,27,29,30,31)(33,37)(38,46)(39,44)(40,47);(25,29)(28,31)(32,34,35,41)(33,38,37,46)(36,45,43,42)(39,47,44,40)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1698, C₂₃×#19155, C₂₃×#19156, …
maximal normal subgroup of	C₂×C₂₃×#1698, C₂₃×#19155, C₂₃×#19156, …
maximal quotient of	C₂₃×#8655, C₂₃×#9224, C₂₃×#9230, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 430);