Finite Group Databasebeta

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C2×D5×#11717942 #30655100

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

Aliases

direct productC2×D5×#11717942
unambiguous semidirect productC5⋊(C22×#11717942)
unambiguous semidirect product(C2×C5)⋊(C2×#11717942)

Splittings

derived, HallC5×C7×C13 ⋊ C22×C9
HallC5×#11717942 ⋊ C22
HallC2×C7×D5×C13 ⋊ C9
HallC2×D5×C13 ⋊ C7⋊C9
HallC2×C7×D5 ⋊ C13⋊C9
HallC7×C13 ⋊ C2×C9×D5
HallC5×C13 ⋊ C22×C7⋊C9
HallC5×C7 ⋊ C22×C13⋊C9
SylowC13 ⋊ C2×D5×C7⋊C9
SylowC7 ⋊ C2×D5×C13⋊C9
SylowC5 ⋊ C22×#11717942

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×#63271
commutator, hypocenterC5×C7×C13C22×C9
FrattiniC3C2×D5×#63271
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C7×D5×C13C3
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 150);