Finite Group Databasebeta

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C17×C11⋊((C5⋊D5)⋊C3) #43242525

order28050
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C5

Aliases

direct productC17×C11⋊((C5⋊D5)⋊C3)
unambiguous semidirect productC11⋊(C17×(C5⋊D5)⋊C3)
unambiguous semidirect product(C5⋊D55)⋊(C3×C17)
unambiguous semidirect product(C17×C5⋊D55)⋊C3

Splittings

Fitting, socle, HallC52×C11×C17 ⋊ C2×C3
derived, HallC52×C11 ⋊ C2×C3×C17
HallC11×C17×C52⋊C3 ⋊ C2
HallC17×C5⋊D55 ⋊ C3
HallC17×C52⋊C3 ⋊ D11
HallC11×C52⋊C3 ⋊ C2×C17
HallC5⋊D55 ⋊ C3×C17
HallC52×C17 ⋊ C3×D11
HallC11×C17 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C17×D11
SylowC52 ⋊ C3×C17×D11
SylowC11 ⋊ C17×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C11⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C11C2×C3×C17
FrattiniC1G
Fitting, socleC52×C11×C17C2×C3
LCSG ▷ C52×C11
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2805

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 50);