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C₇×C₉×D₁₄₅ #32912470

order	18270
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₁₄₅
unambiguous semidirect product	C₅⋊(C₇×C₉×D₂₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₁₄₅
commutator, hypocenter	C₅×C₂₉	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₁₄₅
Fitting	C₅×C₇×C₉×C₂₉	C₂
socle	C₃×C₅×C₇×C₂₉	C₂×C₃
prime radical	C₃×C₇×D₁₄₅	C₃
cosocle	C₃×C₅×C₂₉	C₂×C₃×C₇
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₇×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9135

Conjugacy classes & character table

4662 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×#10596814, C₇×C₉×#10596815, C₉×C₇⋊#10596814, …
maximal normal subgroup of	C₇×C₉×#10596814, C₇×C₉×#10596815, C₉×C₇⋊#10596814, …
maximal quotient of	C₇×C₉×Dic₁₄₅, C₂×C₇×C₉×D₁₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 8);