Finite Group Databasebeta

← Prev (#30655006) Next (#30655008) →

C5×#15692589 #30655007

order16380
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#15692589

Splittings

derived, HallC7×C13 ⋊ C4×C5×C9
HallC5×#11717941 ⋊ C4
HallC5×C7×#261 ⋊ C9
Hall#11717941 ⋊ C4×C5
HallC5×C7×C13 ⋊ C4×C9
HallC7×#261 ⋊ C5×C9
HallC5×#261 ⋊ C7⋊C9
HallC5×C13 ⋊ C4×C7⋊C9
Hall#261 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ #261⋊C9
SylowC13 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C5×#261⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#11763982
commutator, hypocenterC7×C13C4×C5×C9
FrattiniC3C5×#11763982
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13C2×C3
cosocleC3×C7×D13C2×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 57);