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D₃×C₇×D₁₄₅ #27131798

order	12180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×D₁₄₅
unambiguous semidirect product	(C₅×D₃)⋊(C₇×D₂₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₃×D₁₄₅
commutator, hypocenter	C₃×C₅×C₂₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₅×C₂₉
UCS	C₁ ◁ C₇

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1554 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₉×D₁₄₅, D₃×ΓL(1,𝔽₈)×D₁₄₅, C₃×D₃×C₇×D₁₄₅, …
maximal normal subgroup of	D₃×ΓL(1,𝔽₈)×D₁₄₅, C₃×D₃×C₇×D₁₄₅
maximal quotient of	C₇×D₉×D₁₄₅, C₃×D₃×C₇×D₁₄₅, D₃×C₇×D₄₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 133);