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D₇×D₉×C₁₂₁ #44478798

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₂₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×D₉×C₁₂₁
unambiguous semidirect product	(C₇×D₉)⋊(C₂×C₁₂₁)
unambiguous semidirect product	(C₉×D₇)⋊(C₂×C₁₂₁)
unambiguous semidirect product	D₆₃⋊(C₂×C₁₂₁)

Splittings

Fitting, Hall	C₇×C₉×C₁₂₁ ⋊ C₂²
derived, Hall	C₇×C₉ ⋊ C₂²×C₁₂₁
Hall	C₉×C₁₂₁ ⋊ C₂×D₇
Hall	C₇×C₁₂₁ ⋊ C₂×D₉
Sylow	C₉ ⋊ C₂×D₇×C₁₂₁
Sylow	C₇ ⋊ C₂×D₉×C₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₂₁	D₇×D₉
commutator, hypocenter	C₇×C₉	C₂²×C₁₂₁
Frattini	C₃×C₁₁	D₃×C₁₁×D₇
Fitting	C₇×C₉×C₁₂₁	C₂²
socle	C₃×C₇×C₁₁	C₂×D₃×C₁₁
prime radical	C₁₁×D₇×D₉	C₁₁
cosocle	C₇×C₉×C₁₁	C₂²×C₁₁
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₁₂₁

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7623

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 21);