Finite Group Databasebeta

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C2×C7⋊C9×D65 #30655101

order16380
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7⋊C9×D65
unambiguous semidirect product(C2×C5)⋊(D13×C7⋊C9)

Splittings

derived, HallC5×C7×C13 ⋊ C22×C9
HallC5×C13×C7⋊C9 ⋊ C22
HallC2×C7×D65 ⋊ C9
HallC13×C7⋊C9 ⋊ C2×D5
HallC5×C7⋊C9 ⋊ C2×D13
HallC7×C13 ⋊ C2×C9×D5
HallC5×C13 ⋊ C22×C7⋊C9
HallC5×C7 ⋊ C2×C9×D13
SylowC13 ⋊ C2×D5×C7⋊C9
SylowC7 ⋊ C2×C9×D65
SylowC5 ⋊ C2×D13×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D65
commutator, hypocenterC5×C7×C13C22×C9
FrattiniC3C2×ΓL(1,𝔽8)×D65
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C7×D65C3
cosocleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 151);