Finite Group Databasebeta

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C3×C13×C25×D17 #45684121

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C25×D17
unambiguous semidirect productC17⋊(C2×C3×C13×C25)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, SylowC17 ⋊ C2×C3×C13×C25
HallC13×C17×C25 ⋊ C2×C3
HallC3×C17×C25 ⋊ C2×C13
HallC3×C13×C17 ⋊ C2×C25
HallC17×C25 ⋊ C2×C3×C13
HallC13×C17 ⋊ C2×C3×C25
HallC3×C17 ⋊ C2×C13×C25

Subgroups

subgroupG/H
center, hypercenterC3×C13×C25D17
commutator, hypocenterC17C2×C3×C13×C25
FrattiniC5C3×C5×C13×D17
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17C2×C5
prime radicalC3×C5×C13×D17C5
cosocleC5×C17C2×C3×C5×C13
LCSG ▷ C17
UCSC1 ◁ C3×C13×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

9750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 3);