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C₉×D₇×D₁₂₇ #44544675

order	32004
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₇×D₁₂₇

Splittings

Fitting, Hall	C₇×C₉×C₁₂₇ ⋊ C₂²
derived, Hall	C₇×C₁₂₇ ⋊ C₂²×C₉
Hall	C₉×C₁₂₇ ⋊ C₂×D₇
Sylow	C₁₂₇ ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ C₂×D₁₂₇
Sylow	C₇ ⋊ C₂×C₉×D₁₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×D₁₂₇
commutator, hypocenter	C₇×C₁₂₇	C₂²×C₉
Frattini	C₃	C₃×D₇×D₁₂₇
Fitting	C₇×C₉×C₁₂₇	C₂²
socle, cosocle	C₃×C₇×C₁₂₇	C₂²×C₃
prime radical	C₃×D₇×D₁₂₇	C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8001

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 57);