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C25×C17⋊(D13⋊C3) #45684138

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×C17⋊(D13⋊C3)
unambiguous semidirect productC17⋊(C25×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C25×D17)
unambiguous semidirect productD221⋊(C3×C25)
unambiguous semidirect product(C25×D221)⋊C3

Splittings

Fitting, HallC13×C17×C25 ⋊ C2×C3
derived, HallC13×C17 ⋊ C2×C3×C25
HallC17×C25×C13⋊C3 ⋊ C2
HallC25×D221 ⋊ C3
HallC25×C13⋊C3 ⋊ D17
HallC17×C13⋊C3 ⋊ C2×C25
HallD221 ⋊ C3×C25
HallC17×C25 ⋊ D13⋊C3
HallC13×C25 ⋊ C3×D17
HallC13⋊C3 ⋊ C25×D17
SylowC17 ⋊ C25×D13⋊C3
SylowC13 ⋊ C3×C25×D17

Subgroups

subgroupG/H
center, hypercenterC25C17⋊(D13⋊C3)
commutator, hypocenterC13×C17C2×C3×C25
FrattiniC5C5×C17⋊(D13⋊C3)
FittingC13×C17×C25C2×C3
socle, cosocleC5×C13×C17C2×C3×C5
prime radicalC5×C17⋊(D13⋊C3)C5
LCSG ▷ C13×C17
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5525

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 20);