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C₂×(C₄₃⋊C₉)⋊D₇ #24925463

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

Aliases

direct product	C₂×(C₄₃⋊C₉)⋊D₇
unambiguous semidirect product	(C₂×C₄₃⋊C₉)⋊D₇

Splittings

derived, Hall	C₇×C₄₃ ⋊ C₂²×C₉
Hall	C₇×C₄₃⋊C₉ ⋊ C₂²
Hall	C₂×D₃₀₁ ⋊ C₉
Hall	C₄₃⋊C₉ ⋊ C₂×D₇
Sylow	C₄₃ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×D₄₃⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₄₃⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₄₃	C₂²×C₉
Frattini	C₃	C₂×(C₄₃⋊C₃)⋊D₇
Fitting, socle	C₂×C₃×C₇×C₄₃	C₂×C₃
prime radical	C₂×C₃×D₃₀₁	C₃
cosocle	C₃×C₇×C₄₃	C₂²×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 55);