Finite Group Databasebeta

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C₉×D₇×C₂₆₉ #46799829

order	33894
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₆₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₂₆₉

Splittings

Fitting, Hall	C₇×C₉×C₂₆₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₂₆₉
Hall	C₇×C₂₆₉ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₂₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₆₉	D₇
commutator, hypocenter	C₇	C₂×C₉×C₂₆₉
Frattini	C₃	C₃×D₇×C₂₆₉
Fitting	C₇×C₉×C₂₆₉	C₂
socle	C₃×C₇×C₂₆₉	C₂×C₃
prime radical	C₃×D₇×C₂₆₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₂₆₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₂₆₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16947

Conjugacy classes & character table

12105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33894, 4);