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#41×D₉ #63714

order	288
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₉×#41 ⋊ C₂
Sylow	C₉ ⋊ C₂×#41

Subgroups

	subgroup	G/H
center	C₄	C₂²×D₉
commutator, cosocle	C₂×C₉	C₂⁴
Frattini, socle	C₂×C₃	C₂³×D₃
Fitting	C₉×#41	C₂
hypercenter	#41	D₉
hypocenter	C₉	C₂×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ #41

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 4 generators on 17 points:

(2,4)(3,7)(5,8)(6,9);(1,8,9,3,2,4,7,6,5)(10,12,13,16)(11,15,14,17);(11,14)(15,17);(10,11)(12,15)(13,14)(16,17)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×#104, #10588501, D₉×#131, …
maximal normal subgroup of	D₉×#104, #10588501, D₉×#131, …
maximal quotient of	#10589619, D₉×#117, #10589624, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 362);