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C₉×D₇₇⋊D₁₁ #44478955

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₇₇⋊D₁₁

Splittings

Fitting, Hall	C₇×C₉×C₁₁² ⋊ C₂²
derived, Hall	C₇×C₁₁² ⋊ C₂²×C₉
Hall	C₉×C₁₁² ⋊ C₂×D₇
Sylow	C₁₁² ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ D₁₁²
Sylow	C₇ ⋊ C₉×D₁₁²

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇₇⋊D₁₁
commutator, hypocenter	C₇×C₁₁²	C₂²×C₉
Frattini	C₃	C₃×D₇₇⋊D₁₁
Fitting	C₇×C₉×C₁₁²	C₂²
socle, cosocle	C₃×C₇×C₁₁²	C₂²×C₃
prime radical	C₃×D₇₇⋊D₁₁	C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₉

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1386

Conjugacy classes & character table

2115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 178);