Finite Group Databasebeta

← Prev (#28414411) Next (#28414413) →

C17×D435 #28414412

order14790
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D435
unambiguous semidirect productC3⋊(C17×D145)
unambiguous semidirect productC5⋊(C17×D87)
unambiguous semidirect productC29⋊(C17×D15)

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C2
derived, HallC3×C5×C29 ⋊ C2×C17
HallC5×C17×C29 ⋊ D3
HallC3×C17×C29 ⋊ D5
HallC17×C29 ⋊ D15
HallC3×C5×C17 ⋊ D29
HallC5×C29 ⋊ D3×C17
HallC3×C29 ⋊ D5×C17
HallC5×C17 ⋊ D87
HallC3×C17 ⋊ D145
SylowC29 ⋊ C17×D15
HallC3×C5 ⋊ C17×D29
SylowC5 ⋊ C17×D87
SylowC3 ⋊ C17×D145

Subgroups

subgroupG/H
center, hypercenterC17D435
commutator, cosocle, hypocenterC3×C5×C29C2×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C29C2
LCSG ▷ C3×C5×C29
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

3723 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×D15×D29, D17×D435, D493⋊D15, …
maximal normal subgroup ofC17×D15×D29, D17×D435, D493⋊D15, …
maximal quotient ofC17×Dic435, C2×C17×D435

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14790, 14);