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C₅×C₉×D₁₇ #13095248

order	1530
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₉×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₅×C₉)

Splittings

Fitting, Hall	C₅×C₉×C₁₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₅×C₉
Hall	C₉×C₁₇ ⋊ C₂×C₅
Hall	C₅×C₁₇ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₁₇
commutator, hypocenter	C₁₇	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₁₇
Fitting	C₅×C₉×C₁₇	C₂
socle	C₃×C₅×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₁₇	C₃
cosocle	C₃×C₁₇	C₂×C₃×C₅
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₅×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 765

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Conjugacy classes & character table

450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×#595, C₉×#66772, C₅×C₉⋊#595, …
maximal normal subgroup of	C₅×C₉×#595, C₉×#66772, C₅×C₉⋊#595, …
maximal quotient of	C₅×C₉×Dic₁₇, C₂×C₅×C₉×D₁₇, C₅×C₉×C₁₁×D₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1530, 1);