Finite Group Databasebeta

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D3×C13×C17×C25 #45684128

order33150
automorphism?
homologyAbelianization (H1) = C2×C13×C17×C25 · Schur multiplier (H2) = C1

Aliases

direct productD3×C13×C17×C25
unambiguous semidirect productC3⋊(C2×C13×C17×C25)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, SylowC3 ⋊ C2×C13×C17×C25
HallC3×C17×C25 ⋊ C2×C13
HallC3×C13×C25 ⋊ C2×C17
HallC3×C13×C17 ⋊ C2×C25
HallC3×C25 ⋊ C2×C13×C17
HallC3×C17 ⋊ C2×C13×C25
HallC3×C13 ⋊ C2×C17×C25

Subgroups

subgroupG/H
center, hypercenterC13×C17×C25D3
commutator, hypocenterC3C2×C13×C17×C25
FrattiniC5C5×D3×C13×C17
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17C2×C5
prime radicalC5×D3×C13×C17C5
cosocleC3×C5C2×C5×C13×C17
LCSG ▷ C3
UCSC1 ◁ C13×C17×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

16575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 10);