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C13×C25×D51 #45684129

order33150
automorphism?
homologyAbelianization (H1) = C2×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC13×C25×D51
unambiguous semidirect productC3⋊(C13×C25×D17)
unambiguous semidirect productC17⋊(D3×C13×C25)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, HallC3×C17 ⋊ C2×C13×C25
HallC13×C17×C25 ⋊ D3
HallC3×C17×C25 ⋊ C2×C13
HallC3×C13×C25 ⋊ D17
HallC3×C13×C17 ⋊ C2×C25
HallC17×C25 ⋊ D3×C13
HallC13×C17 ⋊ D3×C25
HallC3×C25 ⋊ C13×D17
HallC3×C13 ⋊ C25×D17
SylowC17 ⋊ D3×C13×C25
SylowC3 ⋊ C13×C25×D17

Subgroups

subgroupG/H
center, hypercenterC13×C25D51
commutator, hypocenterC3×C17C2×C13×C25
FrattiniC5C5×C13×D51
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17C2×C5
prime radicalC5×C13×D51C5
cosocleC3×C5×C17C2×C5×C13
LCSG ▷ C3×C17
UCSC1 ◁ C13×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

8775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 11);