Finite Group Databasebeta

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C₇×C₁₉×Dic₆₃ #45691534

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×Dic₆₃
unambiguous semidirect product	C₇⋊(C₇×C₁₉×Dic₉)
unambiguous semidirect product	C₉⋊(C₇×C₁₉×Dic₇)

Splittings

derived	C₇×C₉ ⋊ C₄×C₇×C₁₉
Hall	C₇²×C₉×C₁₉ ⋊ C₄
Hall	C₇²×C₁₉ ⋊ Dic₉
Hall	C₇²×C₉ ⋊ C₄×C₁₉
Hall	C₉×C₁₉ ⋊ C₇×Dic₇
Sylow	C₇² ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₇×C₁₉×Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₉	D₆₃
commutator, hypocenter	C₇×C₉	C₄×C₇×C₁₉
Frattini	C₂×C₃	C₇×C₁₉×D₂₁
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₉	D₃
cosocle	C₂×C₇×C₉	C₂×C₇×C₁₉
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₂×C₇×C₁₉

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

8778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 332);