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C₉×D₇×C₂₉⋊C₇ #38784606

order	25578
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₇×C₂₉⋊C₇
unambiguous semidirect product	(C₉×D₇×C₂₉)⋊C₇

Splittings

Fitting	C₇×C₉×C₂₉ ⋊ C₂×C₇
derived	C₇×C₂₉ ⋊ C₂×C₇×C₉
Hall	C₇×C₉×C₂₉⋊C₇ ⋊ C₂
Hall	C₇×C₂₉⋊C₇ ⋊ C₂×C₉
Hall	C₉×C₂₉ ⋊ C₇×D₇
Sylow	C₂₉ ⋊ C₇×C₉×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×C₂₉⋊C₇
commutator, hypocenter	C₇×C₂₉	C₂×C₇×C₉
Frattini	C₃	C₃×D₇×C₂₉⋊C₇
Fitting	C₇×C₉×C₂₉	C₂×C₇
socle, cosocle	C₃×C₇×C₂₉	C₂×C₃×C₇
prime radical	C₃×D₇×C₂₉⋊C₇	C₃
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₉

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1827

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25578, 50);