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C17×C5⋊(C5⋊(D13⋊C3)) #45684169

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C5

Aliases

direct productC17×C5⋊(C5⋊(D13⋊C3))
unambiguous semidirect productC5⋊(C17×C5⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C17×C5⋊D5)

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derived, HallC52×C13 ⋊ C2×C3×C17
HallC52×C17×C13⋊C3 ⋊ C2
HallC17×C5⋊D65 ⋊ C3
HallC52×C13⋊C3 ⋊ C2×C17
HallC17×C13⋊C3 ⋊ C5⋊D5
HallC5⋊D65 ⋊ C3×C17
HallC52×C17 ⋊ D13⋊C3
HallC13×C17 ⋊ C3×C5⋊D5
HallC13⋊C3 ⋊ C17×C5⋊D5
SylowC52 ⋊ C17×D13⋊C3
SylowC13 ⋊ C3×C17×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC17C5⋊(C5⋊(D13⋊C3))
commutator, cosocle, hypocenterC52×C13C2×C3×C17
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C52×C13
UCSC1 ◁ C17

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5525

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 51);