Finite Group Databasebeta

← Prev (#44477668) Next (#44477670) →

C13×#63118⋊C9 #44477669

order30420
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#63118⋊C9
unambiguous semidirect product#63118⋊(C9×C13)

Splittings

derivedC5×C13 ⋊ C4×C9×C13
HallC5×C13×C13⋊C9 ⋊ C4
HallC13×#63118 ⋊ C9
HallC13×C13⋊C9 ⋊ Dic5
HallC5×C132 ⋊ C4×C9
SylowC132 ⋊ C9×Dic5
SylowC5 ⋊ C13×#261⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C13#63118⋊C3
commutator, hypocenterC5×C13C4×C9×C13
FrattiniC3C13×#63118⋊C3
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×C5×C13×D13C2×C3
cosocleC3×C5×D13C2×C3×C13
LCSG ▷ C5×C13
UCSC1 ◁ C3×C13

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 258);