Finite Group Databasebeta

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C5×(C7⋊C9)⋊#261 #30655005

order16380
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C7⋊C9)⋊#261
unambiguous semidirect product(C7⋊C9)⋊(C5×#261)

Splittings

derived, HallC7×C13 ⋊ C4×C5×C9
HallC5×C13×C7⋊C9 ⋊ C4
HallC5×C7⋊#261 ⋊ C9
HallC13×C7⋊C9 ⋊ C4×C5
HallC5×C7×C13 ⋊ C4×C9
HallC7⋊#261 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ #261
HallC5×C13 ⋊ Dic7⋊C9
HallC7⋊C9 ⋊ C5×#261
HallC5×C7 ⋊ C9×#261
SylowC13 ⋊ C5×Dic7⋊C9
SylowC7 ⋊ C5×C9×#261

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊#261
commutator, hypocenterC7×C13C4×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)⋊#261
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13C2×C3
cosocleC3×C7×D13C2×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 55);