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D₃×D₁₅×C₄₁ #20301642

order	7380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₁₅×C₄₁
unambiguous semidirect product	(C₃×D₃)⋊(D₅×C₄₁)
unambiguous semidirect product	(C₅×D₃)⋊(D₃×C₄₁)

Splittings

Fitting, socle, Hall	C₃²×C₅×C₄₁ ⋊ C₂²
derived, Hall	C₃²×C₅ ⋊ C₂²×C₄₁
Hall	C₃²×C₄₁ ⋊ C₂×D₅
Hall	C₅×C₄₁ ⋊ D₃²
Sylow	C₃² ⋊ C₂×D₅×C₄₁
Sylow	C₅ ⋊ D₃²×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	D₃×D₁₅
commutator, hypocenter	C₃²×C₅	C₂²×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₄₁	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₄₁

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1107 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₄₁×D₇₅, D₃×D₁₅×C₄₁⋊C₅, C₅×D₃×D₁₅×C₄₁, …
maximal normal subgroup of	D₃×D₁₅×C₄₁⋊C₅, C₅×D₃×D₁₅×C₄₁
maximal quotient of	D₃×C₄₁×D₇₅, C₅×D₃×D₁₅×C₄₁, D₁₅²×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 120);