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C₉×#1455 #11766176

order	1152
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₉ · Schur multiplier (H₂) = C₈

Aliases

Subgroups

	subgroup	G/H
center	C₄²×C₉	C₂³
commutator	C₂²	C₂×C₄²×C₉
Frattini, cosocle	C₃×C₄²	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₄²
prime radical	C₂³×C₃	C₃×C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ 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)(10,11,12,15,13,14,16,17);(18,19,20,23,21,22,24,25);(11,14)(15,17)(19,22)(23,25)

Conjugacy classes & character table

504 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₉×#1455, #72244509
maximal subgroup of	D₉×#1455, C₉×#19745, #72244509, …
maximal normal subgroup of	D₉×#1455, C₉×#19745, #72244509, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 187);