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C5×C13×D255 #45684192

order33150
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D255
unambiguous semidirect productC3⋊(C5×C13×D85)
unambiguous semidirect productC5⋊(C5×C13×D51)
unambiguous semidirect productC17⋊(C5×C13×D15)

Splittings

Fitting, socle, HallC3×C52×C13×C17 ⋊ C2
derivedC3×C5×C17 ⋊ C2×C5×C13
HallC52×C13×C17 ⋊ D3
HallC3×C52×C17 ⋊ C2×C13
HallC3×C52×C13 ⋊ D17
HallC3×C13×C17 ⋊ C5×D5
HallC52×C17 ⋊ D3×C13
HallC52×C13 ⋊ D51
HallC13×C17 ⋊ C5×D15
HallC3×C52 ⋊ C13×D17
HallC3×C17 ⋊ C5×D5×C13
HallC3×C13 ⋊ C5×D85
SylowC52 ⋊ C13×D51
SylowC17 ⋊ C5×C13×D15
SylowC3 ⋊ C5×C13×D85

Subgroups

subgroupG/H
center, hypercenterC5×C13D255
commutator, cosocle, hypocenterC3×C5×C17C2×C5×C13
FrattiniC1G
Fitting, socleC3×C52×C13×C17C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

Conjugacy classes & character table

8385 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 74);