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C₂×(C₆₇⋊C₉)⋊D₇ #30683071

order	16884
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₆₇⋊C₉)⋊D₇
unambiguous semidirect product	(C₂×C₆₇⋊C₉)⋊D₇

Splittings

derived, Hall	C₇×C₆₇ ⋊ C₂²×C₉
Hall	C₇×C₆₇⋊C₉ ⋊ C₂²
Hall	C₂×D₄₆₉ ⋊ C₉
Hall	C₆₇⋊C₉ ⋊ C₂×D₇
Sylow	C₆₇ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×D₆₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₆₇⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₆₇	C₂²×C₉
Frattini	C₃	C₂×(C₆₇⋊C₃)⋊D₇
Fitting, socle	C₂×C₃×C₇×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₄₆₉	C₃
cosocle	C₃×C₇×C₆₇	C₂²×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 40);