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C₉×D₇×D₄₃ #24925465

order	10836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₇×D₄₃

Splittings

Fitting, Hall	C₇×C₉×C₄₃ ⋊ C₂²
derived, Hall	C₇×C₄₃ ⋊ C₂²×C₉
Hall	C₉×C₄₃ ⋊ C₂×D₇
Hall	C₇×C₉ ⋊ C₂×D₄₃
Sylow	C₄₃ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×C₉×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×D₄₃
commutator, hypocenter	C₇×C₄₃	C₂²×C₉
Frattini	C₃	C₃×D₇×D₄₃
Fitting	C₇×C₉×C₄₃	C₂²
socle, cosocle	C₃×C₇×C₄₃	C₂²×C₃
prime radical	C₃×D₇×D₄₃	C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 57);