C₂₃×#575 #13092124

order	1472
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#575

Subgroups

	subgroup	G/H
center	C₄×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂²×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

262 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 4 generators on 39 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)(26,33)(27,32)(28,36)(29,31)(30,34)(35,39)(37,38);(24,26)(25,30)(27,34)(28,37)(29,35)(31,38)(32,39)(33,36);(25,31)(30,38)(32,36)(33,39);(24,27,29,28)(25,32,31,36)(26,34,35,37)(30,39,38,33)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15673761, #15673900, #15674447, …
maximal subgroup of	C₂₃×#1881, C₂₃×#1906, C₂₃×#2008, …
maximal normal subgroup of	C₂₃×#1881, C₂₃×#1906, C₂₃×#2008, …
maximal quotient of	C₂₃×#2896, C₂₃×#2911, C₂₃×#2943, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 256);