Finite Group Databasebeta

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C25×D17×C13⋊C3 #45684136

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

Aliases

direct productC25×D17×C13⋊C3
unambiguous semidirect productC17⋊(C2×C25×C13⋊C3)
unambiguous semidirect product(C13×D17)⋊(C3×C25)
unambiguous semidirect product(C13×C25×D17)⋊C3

Splittings

Fitting, HallC13×C17×C25 ⋊ C2×C3
derived, HallC13×C17 ⋊ C2×C3×C25
HallC17×C25×C13⋊C3 ⋊ C2
HallC13×C25×D17 ⋊ C3
HallC17×C13⋊C3 ⋊ C2×C25
HallC13×D17 ⋊ C3×C25
HallC17×C25 ⋊ C2×C13⋊C3
HallC13×C25 ⋊ C3×D17
SylowC17 ⋊ C2×C25×C13⋊C3
SylowC13 ⋊ C3×C25×D17

Subgroups

subgroupG/H
center, hypercenterC25D17×C13⋊C3
commutator, hypocenterC13×C17C2×C3×C25
FrattiniC5C5×D17×C13⋊C3
FittingC13×C17×C25C2×C3
socle, cosocleC5×C13×C17C2×C3×C5
prime radicalC5×D17×C13⋊C3C5
LCSG ▷ C13×C17
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5525

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 18);