Finite Group Databasebeta

← Prev (#26043350) Next (#26043352) →

C5×#63120⋊C9 #26043351

order11700
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63120⋊C9
unambiguous semidirect product#63120⋊(C5×C9)
unambiguous semidirect product(C5×#63120)⋊C9

Splittings

derivedC5×C13 ⋊ C4×C5×C9
HallC52×C13⋊C9 ⋊ C4
HallC5×#63120 ⋊ C9
HallC52×C13 ⋊ C4×C9
HallC13⋊C9 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ Dic13⋊C9
SylowC13 ⋊ C5×C9×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC3×C5#63120⋊C3
commutator, hypocenterC5×C13C4×C5×C9
FrattiniC3C5×#63120⋊C3
Fitting, socleC3×C52×C13C3×C4
prime radicalC3×C5×D5×C13C2×C3
cosocleC3×D5×C13C2×C3×C5
LCSG ▷ C5×C13
UCSC1 ◁ C3×C5

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 198);