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C13×C3⋊(C5⋊D85) #45684196

order33150
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C5

Aliases

direct productC13×C3⋊(C5⋊D85)
unambiguous semidirect productC3⋊(C13×C5⋊D85)
unambiguous semidirect productC5⋊(C13×D255)
unambiguous semidirect productC17⋊(C13×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C13×C17 ⋊ C2
derived, HallC3×C52×C17 ⋊ C2×C13
HallC52×C13×C17 ⋊ D3
HallC3×C52×C13 ⋊ D17
HallC3×C13×C17 ⋊ C5⋊D5
HallC52×C17 ⋊ D3×C13
HallC52×C13 ⋊ D51
HallC13×C17 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C13×D17
HallC3×C17 ⋊ C13×C5⋊D5
HallC3×C13 ⋊ C5⋊D85
SylowC52 ⋊ C13×D51
SylowC17 ⋊ C13×C3⋊(C5⋊D5)
SylowC3 ⋊ C13×C5⋊D85

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(C5⋊D85)
commutator, cosocle, hypocenterC3×C52×C17C2×C13
FrattiniC1G
Fitting, socleC3×C52×C13×C17C2
LCSG ▷ C3×C52×C17
UCSC1 ◁ C13

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

8307 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 78);