Finite Group Databasebeta

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C5×#13109896⋊C2 #30655003

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

Aliases

direct productC5×#13109896⋊C2
unambiguous semidirect product#13109896⋊(C2×C5)
unambiguous semidirect product#13109900⋊(C2×C5)
unambiguous semidirect product#13109902⋊(C2×C5)

Splittings

derived, HallC7×C13 ⋊ C22×C5×C9
HallC5×#11717941 ⋊ C22
HallC5×D7×D13 ⋊ C9
Hall#11717941 ⋊ C22×C5
HallC5×C7×C13 ⋊ C22×C9
HallD7×D13 ⋊ C5×C9
HallC5×C13 ⋊ C2×D7⋊C9
HallC5×C7 ⋊ C2×D13⋊C9
SylowC13 ⋊ C2×C5×D7⋊C9
SylowC7 ⋊ C2×C5×D13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#10587716⋊C2
commutator, hypocenterC7×C13C22×C5×C9
FrattiniC3C5×#10587716⋊C2
Fitting, socleC3×C5×C7×C13C22×C3
prime radicalC3×C5×D7×D13C3
cosocleC3×C7×C13C22×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 53);