Finite Group Databasebeta

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C11×C17×C3⋊(C5⋊D5) #43242548

order28050
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C5

Aliases

direct productC11×C17×C3⋊(C5⋊D5)
unambiguous semidirect productC3⋊(C11×C17×C5⋊D5)
unambiguous semidirect productC5⋊(C11×C17×D15)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, HallC3×C52 ⋊ C2×C11×C17
HallC52×C11×C17 ⋊ D3
HallC3×C52×C17 ⋊ C2×C11
HallC3×C52×C11 ⋊ C2×C17
HallC3×C11×C17 ⋊ C5⋊D5
HallC52×C17 ⋊ D3×C11
HallC52×C11 ⋊ D3×C17
HallC3×C17 ⋊ C11×C5⋊D5
HallC3×C11 ⋊ C17×C5⋊D5
SylowC52 ⋊ D3×C11×C17
SylowC3 ⋊ C11×C17×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC11×C17C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52C2×C11×C17
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C3×C52
UCSC1 ◁ C11×C17

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

7293 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 73);