C₂₃×#1720 #15669339

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₂₃×#1720

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)(24,25,29,26)(27,28,31,30)(32,33,36,39)(34,40,42,47)(35,44,41,38)(37,45,46,43);(24,26,28,31,29,25,30,27)(32,34,41,45,36,42,35,43)(33,37,44,47,39,46,38,40);(24,27,28,26,29,31,30,25)(34,42)(37,46)(40,47)(43,45)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1720, C₂₃×#19613, C₂₃×#19619, …
maximal normal subgroup of	C₂×C₂₃×#1720, C₂₃×#19613, C₂₃×#19619, …
maximal quotient of	C₂₃×#8821, C₂₃×#9827, C₂₃×#9828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 452);