Finite Group Databasebeta

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C2×C5×C7×C9×D13 #30655172

order16380
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×C9×D13

Splittings

FittingC2×C5×C7×C9×C13 ⋊ C2
derived, SylowC13 ⋊ C22×C5×C7×C9
HallC5×C7×C9×C13 ⋊ C22
HallC7×C9×C13 ⋊ C22×C5
HallC5×C9×C13 ⋊ C22×C7
HallC5×C7×C13 ⋊ C22×C9
HallC9×C13 ⋊ C22×C5×C7
HallC7×C13 ⋊ C22×C5×C9
HallC5×C13 ⋊ C22×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C9D13
commutator, hypocenterC13C22×C5×C7×C9
FrattiniC3C2×C3×C5×C7×D13
FittingC2×C5×C7×C9×C13C2
socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C7×D13C3
cosocleC3×C13C22×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C2×C5×C7×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

5040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 222);