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C13⋊C3×C5⋊D85 #45684172

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

Aliases

direct productC13⋊C3×C5⋊D85
unambiguous semidirect productC5⋊(C13⋊C3×D85)
unambiguous semidirect productC17⋊(C13⋊C3×C5⋊D5)

Splittings

Fitting, socle, derived, HallC52×C13×C17 ⋊ C2×C3
HallC52×C17×C13⋊C3 ⋊ C2
HallC13×C5⋊D85 ⋊ C3
HallC52×C13⋊C3 ⋊ D17
HallC17×C13⋊C3 ⋊ C5⋊D5
HallC52×C17 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C3×D17
HallC13×C17 ⋊ C3×C5⋊D5
SylowC52 ⋊ D17×C13⋊C3
SylowC17 ⋊ C13⋊C3×C5⋊D5
SylowC13 ⋊ C3×C5⋊D85

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5525

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 54);