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D17×C13⋊(C52⋊C3) #45684147

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

Aliases

direct productD17×C13⋊(C52⋊C3)
unambiguous semidirect productC17⋊(C2×C13⋊(C52⋊C3))
unambiguous semidirect product(C13×D17)⋊(C52⋊C3)
unambiguous semidirect product(C52×D17)⋊(C13⋊C3)

Splittings

Fitting, socle, derived, HallC52×C13×C17 ⋊ C2×C3
HallC17×C13⋊(C52⋊C3) ⋊ C2
HallC52×C13×D17 ⋊ C3
HallC52×D17 ⋊ C13⋊C3
HallC13×D17 ⋊ C52⋊C3
HallC52×C17 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C3×D17
HallC13×C17 ⋊ C2×C52⋊C3
SylowC52 ⋊ D17×C13⋊C3
SylowC17 ⋊ C2×C13⋊(C52⋊C3)
SylowC13 ⋊ D17×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C17C2×C3
LCSG ▷ C52×C13×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 29);