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C17×D465 #30629036

order15810
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D465
unambiguous semidirect productC3⋊(C17×D155)
unambiguous semidirect productC5⋊(C17×D93)
unambiguous semidirect productC31⋊(C17×D15)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, HallC3×C5×C31 ⋊ C2×C17
HallC5×C17×C31 ⋊ D3
HallC3×C17×C31 ⋊ D5
HallC17×C31 ⋊ D15
HallC3×C5×C17 ⋊ D31
HallC5×C31 ⋊ D3×C17
HallC3×C31 ⋊ D5×C17
HallC5×C17 ⋊ D93
HallC3×C17 ⋊ D155
SylowC31 ⋊ C17×D15
HallC3×C5 ⋊ C17×D31
SylowC5 ⋊ C17×D93
SylowC3 ⋊ C17×D155

Subgroups

subgroupG/H
center, hypercenterC17D465
commutator, cosocle, hypocenterC3×C5×C31C2×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C3×C5×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3978 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×D15×D31, D17×D465, D527⋊D15, …
maximal normal subgroup ofC17×D15×D31, D17×D465, D527⋊D15, …
maximal quotient ofC17×Dic465, C2×C17×D465

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 17);