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C5×D1581 #30629034

order15810
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1581
unambiguous semidirect productC3⋊(C5×D527)
unambiguous semidirect productC17⋊(C5×D93)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, HallC3×C17×C31 ⋊ C2×C5
HallC5×C17×C31 ⋊ D3
HallC17×C31 ⋊ C5×D3
HallC3×C5×C31 ⋊ D17
HallC3×C5×C17 ⋊ D31
HallC5×C31 ⋊ D51
HallC3×C31 ⋊ C5×D17
HallC5×C17 ⋊ D93
HallC3×C17 ⋊ C5×D31
SylowC31 ⋊ C5×D51
SylowC17 ⋊ C5×D93
HallC3×C5 ⋊ D527
SylowC3 ⋊ C5×D527

Subgroups

subgroupG/H
center, hypercenterC5D1581
commutator, cosocle, hypocenterC3×C17×C31C2×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C3×C17×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D31×D51, C5×D17×D93, C5×D3×D527, …
maximal normal subgroup ofC5×D31×D51, C5×D17×D93, C5×D3×D527, …
maximal quotient ofC5×Dic1581, C2×C5×D1581

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 15);