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C₉×D₁₂₇₃ #37523823

order	22914
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₂₇₃

Splittings

Fitting, Hall	C₉×C₁₉×C₆₇ ⋊ C₂
derived, Hall	C₁₉×C₆₇ ⋊ C₂×C₉
Hall	C₉×C₆₇ ⋊ D₁₉
Hall	C₉×C₁₉ ⋊ D₆₇
Sylow	C₆₇ ⋊ C₉×D₁₉
Sylow	C₁₉ ⋊ C₉×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₂₇₃
commutator, hypocenter	C₁₉×C₆₇	C₂×C₉
Frattini	C₃	C₃×D₁₂₇₃
Fitting	C₉×C₁₉×C₆₇	C₂
socle, cosocle	C₃×C₁₉×C₆₇	C₂×C₃
prime radical	C₃×D₁₂₇₃	C₃
LCS	G ▷ C₁₉×C₆₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11457

Conjugacy classes & character table

5742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22914, 8);