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D₃×C₇×D₅×C₁₉ #22547724

order	7980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×D₅×C₁₉
unambiguous semidirect product	(C₅×D₃)⋊(C₂×C₇×C₁₉)
unambiguous semidirect product	(C₃×D₅)⋊(C₂×C₇×C₁₉)
unambiguous semidirect product	D₁₅⋊(C₂×C₇×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₅×D₉×C₁₉, D₃×C₇×D₅×C₁₉⋊C₃, D₃×D₅×C₁₉×ΓL(1,𝔽₈), …
maximal normal subgroup of	D₃×C₇×D₅×C₁₉⋊C₃, D₃×D₅×C₁₉×ΓL(1,𝔽₈), D₃×D₅×#87704, …
maximal quotient of	C₇×D₅×D₉×C₁₉, C₃×D₃×C₇×D₅×C₁₉, D₃×C₇×C₁₉×D₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 149);