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C5×C5⋊(C17⋊(D13⋊C3)) #45684166

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊(C17⋊(D13⋊C3))
unambiguous semidirect productC5⋊(C5×C17⋊(D13⋊C3))
unambiguous semidirect productC17⋊(C5×C5⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C5×D85)
unambiguous semidirect productD1105⋊(C3×C5)
unambiguous semidirect product(C5×D1105)⋊C3

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derivedC5×C13×C17 ⋊ C2×C3×C5
HallC52×C17×C13⋊C3 ⋊ C2
HallC5×D1105 ⋊ C3
HallC52×C13⋊C3 ⋊ D17
HallC17×C13⋊C3 ⋊ C5×D5
HallC52×C17 ⋊ D13⋊C3
HallC52×C13 ⋊ C3×D17
HallC13×C17 ⋊ C3×C5×D5
HallC13⋊C3 ⋊ C5×D85
SylowC52 ⋊ C17⋊(D13⋊C3)
SylowC17 ⋊ C5×C5⋊(D13⋊C3)
SylowC13 ⋊ C3×C5×D85

Subgroups

subgroupG/H
center, hypercenterC5C5⋊(C17⋊(D13⋊C3))
commutator, cosocle, hypocenterC5×C13×C17C2×C3×C5
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2210

Conjugacy classes & character table

1510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 48);