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C17×C3⋊(C5⋊D55) #43242550

order28050
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C5

Aliases

direct productC17×C3⋊(C5⋊D55)
unambiguous semidirect productC3⋊(C17×C5⋊D55)
unambiguous semidirect productC5⋊(C17×D165)
unambiguous semidirect productC11⋊(C17×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, HallC3×C52×C11 ⋊ C2×C17
HallC52×C11×C17 ⋊ D3
HallC3×C52×C17 ⋊ D11
HallC3×C11×C17 ⋊ C5⋊D5
HallC52×C17 ⋊ D33
HallC52×C11 ⋊ D3×C17
HallC11×C17 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C17×D11
HallC3×C17 ⋊ C5⋊D55
HallC3×C11 ⋊ C17×C5⋊D5
SylowC52 ⋊ C17×D33
SylowC11 ⋊ C17×C3⋊(C5⋊D5)
SylowC3 ⋊ C17×C5⋊D55

Subgroups

subgroupG/H
center, hypercenterC17C3⋊(C5⋊D55)
commutator, cosocle, hypocenterC3×C52×C11C2×C17
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C3×C52×C11
UCSC1 ◁ C17

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

7038 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 75);