Finite Group Databasebeta

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C22×C5×C7×C13⋊C9 #30655163

order16380
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C7×C13⋊C9

Splittings

derived, SylowC13 ⋊ C22×C5×C7×C9
HallC22×C5×C7×C13 ⋊ C9
HallC5×C7×C13 ⋊ C22×C9
HallC22×C7×C13 ⋊ C5×C9
HallC22×C5×C13 ⋊ C7×C9
HallC7×C13 ⋊ C22×C5×C9
HallC5×C13 ⋊ C22×C7×C9
HallC22×C13 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5×C7C13⋊C3
commutator, hypocenterC13C22×C5×C7×C9
FrattiniC3C22×C5×C7×C13⋊C3
Fitting, socle, prime radicalC22×C3×C5×C7×C13C3
cosocleC3×C13C22×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C22×C3×C5×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16380

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 213);