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C13×D1275 #45684133

order33150
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1275
unambiguous semidirect productC3⋊(C13×D425)
unambiguous semidirect productC17⋊(C13×D75)
unambiguous semidirect productC25⋊(C13×D51)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, HallC3×C17×C25 ⋊ C2×C13
HallC13×C17×C25 ⋊ D3
HallC3×C13×C25 ⋊ D17
HallC3×C13×C17 ⋊ D25
HallC17×C25 ⋊ D3×C13
HallC13×C25 ⋊ D51
HallC13×C17 ⋊ D75
HallC3×C25 ⋊ C13×D17
HallC3×C17 ⋊ C13×D25
HallC3×C13 ⋊ D425
SylowC25 ⋊ C13×D51
SylowC17 ⋊ C13×D75
SylowC3 ⋊ C13×D425

Subgroups

subgroupG/H
center, hypercenterC13D1275
commutator, cosocle, hypocenterC3×C17×C25C2×C13
FrattiniC5C13×D255
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17D5
LCSG ▷ C3×C17×C25
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

8307 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 15);