Finite Group Databasebeta

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C₉×C₁₉×D₇₇ #39911784

order	26334
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×D₇₇
unambiguous semidirect product	C₁₁⋊(C₉×D₇×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₇₇
commutator, hypocenter	C₇×C₁₁	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₇₇
Fitting	C₇×C₉×C₁₁×C₁₉	C₂
socle	C₃×C₇×C₁₁×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×D₇₇	C₃
cosocle	C₃×C₇×C₁₁	C₂×C₃×C₁₉
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₉×C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13167

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 11);