Finite Group Databasebeta

← Prev (#31821747) Next (#31821749) →

C5×C7×C17×D15 #31821748

order17850
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C17×D15
unambiguous semidirect productC3⋊(C5×C7×D5×C17)
unambiguous semidirect productC5⋊(C5×D3×C7×C17)

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C2
derivedC3×C5 ⋊ C2×C5×C7×C17
HallC52×C7×C17 ⋊ D3
HallC3×C52×C17 ⋊ C2×C7
HallC3×C52×C7 ⋊ C2×C17
HallC52×C17 ⋊ D3×C7
HallC3×C7×C17 ⋊ C5×D5
HallC52×C7 ⋊ D3×C17
HallC3×C52 ⋊ C2×C7×C17
HallC3×C17 ⋊ C5×C7×D5
SylowC52 ⋊ D3×C7×C17
HallC3×C7 ⋊ C5×D5×C17
SylowC3 ⋊ C5×C7×D5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C7×C17D15
commutator, cosocle, hypocenterC3×C5C2×C5×C7×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C2
LCSG ▷ C3×C5
UCSC1 ◁ C5×C7×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

5355 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D15×D17, C5×D7×C17×D15, C5×D15×D119, …
maximal normal subgroup ofC5×C7×D15×D17, C5×D7×C17×D15, C5×D15×D119, …
maximal quotient ofC5×C7×C17×Dic15, C2×C5×C7×C17×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17850, 65);