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C11×C3⋊(C5⋊D85) #43242549

order28050
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C3⋊(C5⋊D85)
unambiguous semidirect productC3⋊(C11×C5⋊D85)
unambiguous semidirect productC5⋊(C11×D255)
unambiguous semidirect productC17⋊(C11×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, HallC3×C52×C17 ⋊ C2×C11
HallC52×C11×C17 ⋊ D3
HallC3×C52×C11 ⋊ D17
HallC3×C11×C17 ⋊ C5⋊D5
HallC52×C17 ⋊ D3×C11
HallC52×C11 ⋊ D51
HallC11×C17 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C11×D17
HallC3×C17 ⋊ C11×C5⋊D5
HallC3×C11 ⋊ C5⋊D85
SylowC52 ⋊ C11×D51
SylowC17 ⋊ C11×C3⋊(C5⋊D5)
SylowC3 ⋊ C11×C5⋊D85

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C5⋊D85)
commutator, cosocle, hypocenterC3×C52×C17C2×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C3×C52×C17
UCSC1 ◁ C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

7029 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 74);