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C22×C5×#11717941 #30655165

order16380
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×#11717941

Splittings

derived, HallC7×C13 ⋊ C22×C5×C9
HallC22×C5×C7×C13 ⋊ C9
HallC5×C7×C13 ⋊ C22×C9
HallC22×C7×C13 ⋊ C5×C9
HallC22×C5×C13 ⋊ C7⋊C9
HallC22×C5×C7 ⋊ C13⋊C9
HallC5×C13 ⋊ C22×C7⋊C9
HallC22×C13 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C22×C13⋊C9
HallC22×C7 ⋊ C5×C13⋊C9
SylowC13 ⋊ C22×C5×C7⋊C9
SylowC7 ⋊ C22×C5×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5#63270
commutator, hypocenterC7×C13C22×C5×C9
FrattiniC3C22×C5×#63270
Fitting, socle, prime radicalC22×C3×C5×C7×C13C3
cosocleC3×C7×C13C22×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C22×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16380

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 215);