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C52×C17×D13⋊C3 #45684162

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C17 · Schur multiplier (H2) = C5

Aliases

direct productC52×C17×D13⋊C3
unambiguous semidirect productD13⋊(C3×C52×C17)
unambiguous semidirect product(C13⋊C3)⋊(C2×C52×C17)
unambiguous semidirect product(C5×D13)⋊(C3×C5×C17)
unambiguous semidirect product(C17×D13)⋊(C3×C52)
unambiguous semidirect product(C5×C17×D13)⋊(C3×C5)

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C52×C17
HallC52×C17×C13⋊C3 ⋊ C2
HallC52×C17×D13 ⋊ C3
HallC52×C13⋊C3 ⋊ C2×C17
HallC17×C13⋊C3 ⋊ C2×C52
HallC52×D13 ⋊ C3×C17
HallC17×D13 ⋊ C3×C52
HallC52×C13 ⋊ C2×C3×C17
HallC13×C17 ⋊ C2×C3×C52
HallC13⋊C3 ⋊ C2×C52×C17
HallD13 ⋊ C3×C52×C17

Subgroups

subgroupG/H
center, hypercenterC52×C17D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C52×C17
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C13
UCSC1 ◁ C52×C17

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5525

Conjugacy classes & character table

3400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 44);