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C52×D17×C13⋊C3 #45684164

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

Aliases

direct productC52×D17×C13⋊C3
unambiguous semidirect productC17⋊(C2×C52×C13⋊C3)
unambiguous semidirect product(C13×D17)⋊(C3×C52)
unambiguous semidirect product(C5×C13×D17)⋊(C3×C5)

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derived, HallC13×C17 ⋊ C2×C3×C52
HallC52×C17×C13⋊C3 ⋊ C2
HallC52×C13×D17 ⋊ C3
HallC17×C13⋊C3 ⋊ C2×C52
HallC13×D17 ⋊ C3×C52
HallC52×C17 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C3×D17
SylowC17 ⋊ C2×C52×C13⋊C3
SylowC13 ⋊ C3×C52×D17

Subgroups

subgroupG/H
center, hypercenterC52D17×C13⋊C3
commutator, cosocle, hypocenterC13×C17C2×C3×C52
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C13×C17
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5525

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 46);