Finite Group Databasebeta

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C₇×C₁₉×D₃₃ #22578613

order	8778
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×D₃₃
unambiguous semidirect product	C₃⋊(C₇×C₁₉×D₁₁)
unambiguous semidirect product	C₁₁⋊(D₃×C₇×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₃₃
commutator, hypocenter	C₃×C₁₁	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₇×C₁₉

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₁₉×D₃₃, D₃×C₇×C₁₉×D₁₁, C₇×D₃₃⋊D₁₉, …
maximal normal subgroup of	C₇×D₁₉×D₃₃, D₃×C₇×C₁₉×D₁₁, C₇×D₃₃⋊D₁₉, …
maximal quotient of	C₇×C₁₉×Dic₃₃, C₂×C₇×C₁₉×D₃₃, C₇×C₁₉×D₉₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 15);