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C₂×C₉×D₈₄₇ #44478807

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

Aliases

direct product	C₂×C₉×D₈₄₇
unambiguous semidirect product	(C₂×C₁₂₁)⋊(C₉×D₇)

Splittings

Fitting	C₂×C₇×C₉×C₁₂₁ ⋊ C₂
derived, Hall	C₇×C₁₂₁ ⋊ C₂²×C₉
Hall	C₇×C₉×C₁₂₁ ⋊ C₂²
Hall	C₉×C₁₂₁ ⋊ C₂×D₇
Sylow	C₁₂₁ ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ C₂×D₁₂₁
Sylow	C₇ ⋊ C₂×C₉×D₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₈₄₇
commutator, hypocenter	C₇×C₁₂₁	C₂²×C₉
Frattini	C₃×C₁₁	C₂×C₃×D₇₇
Fitting	C₂×C₇×C₉×C₁₂₁	C₂
socle	C₂×C₃×C₇×C₁₁	C₃×D₁₁
prime radical	C₂×C₃×D₈₄₇	C₃
cosocle	C₃×C₇×C₁₂₁	C₂²×C₃
LCS	G ▷ C₇×C₁₂₁
UCS	C₁ ◁ C₂×C₉

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15246

Conjugacy classes & character table

7650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 30);