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C₉×#1705 #11766426

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₈

Aliases

Subgroups

	subgroup	G/H
center	C₂²×C₉	#127
commutator	C₄²	C₂³×C₉
Frattini, cosocle	C₃×C₄²	C₂³×C₃
socle	C₂²×C₃	C₃×#127
prime radical	C₃×#127	C₂²×C₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ G

321 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5,6,7,8,9)(11,14)(12,16)(15,17)(19,22)(20,24)(23,25);(10,11,12,14,13,15,16,17);(18,19,20,22,21,23,24,25)

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₉×#1705, #72244495
maximal subgroup of	D₉×#1705, C₉×#19745, #72244495, …
maximal normal subgroup of	D₉×#1705, C₉×#19745, #72244495, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 437);