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C₇×C₉×D₇×C₂₉ #38784635

order	25578
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

C₇×C₉×D₇×C₂₉

Splittings

Fitting, Hall	C₇²×C₉×C₂₉ ⋊ C₂
derived	C₇ ⋊ C₂×C₇×C₉×C₂₉
Hall	C₇²×C₂₉ ⋊ C₂×C₉
Hall	C₇²×C₉ ⋊ C₂×C₂₉
Sylow	C₇² ⋊ C₂×C₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉×C₂₉	D₇
commutator, hypocenter	C₇	C₂×C₇×C₉×C₂₉
Frattini	C₃	C₃×C₇×D₇×C₂₉
Fitting	C₇²×C₉×C₂₉	C₂
socle	C₃×C₇²×C₂₉	C₂×C₃
prime radical	C₃×C₇×D₇×C₂₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₇×C₂₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₇×C₉×C₂₉

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3654

Conjugacy classes & character table

9135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25578, 79);