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C₂×C₉×D₆₂₃ #36375856

order	22428
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₆₂₃
unambiguous semidirect product	(C₂×C₈₉)⋊(C₉×D₇)

Splittings

Fitting	C₂×C₇×C₉×C₈₉ ⋊ C₂
derived, Hall	C₇×C₈₉ ⋊ C₂²×C₉
Hall	C₇×C₉×C₈₉ ⋊ C₂²
Hall	C₉×C₈₉ ⋊ C₂×D₇
Sylow	C₈₉ ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ C₂×D₈₉
Sylow	C₇ ⋊ C₂×C₉×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₆₂₃
commutator, hypocenter	C₇×C₈₉	C₂²×C₉
Frattini	C₃	C₂×C₃×D₆₂₃
Fitting	C₂×C₇×C₉×C₈₉	C₂
socle	C₂×C₃×C₇×C₈₉	C₂×C₃
prime radical	C₂×C₃×D₆₂₃	C₃
cosocle	C₃×C₇×C₈₉	C₂²×C₃
LCS	G ▷ C₇×C₈₉
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11214

Conjugacy classes & character table

5634 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22428, 38);