C₂₃×#2016 #15669635

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2016

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

370 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 2944

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7405, C₂₃×#7756, C₂₃×#7757, …
maximal normal subgroup of	C₂₃×#7405, C₂₃×#7756, C₂₃×#7757, …
maximal quotient of	C₂₃×#9957, C₂₃×#9959, C₂₃×#9967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 748);