Finite Group Databasebeta

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C5×C11⋊C5×D51 #43242511

order28050
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×D51
unambiguous semidirect productC3⋊(C5×D17×C11⋊C5)
unambiguous semidirect productC17⋊(C5×D3×C11⋊C5)
unambiguous semidirect product(C11×D51)⋊C52
unambiguous semidirect product(C5×C11×D51)⋊C5

Splittings

Fitting, socleC3×C5×C11×C17 ⋊ C2×C5
derived, HallC3×C11×C17 ⋊ C2×C52
HallC3×C5×C17×C11⋊C5 ⋊ C2
HallC5×C17×C11⋊C5 ⋊ D3
HallC11×D51 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ D17
HallC11×C17 ⋊ C52×D3
HallC3×C17 ⋊ C2×C5×C11⋊C5
HallC3×C11 ⋊ C52×D17
SylowC17 ⋊ C5×D3×C11⋊C5
SylowC11 ⋊ C52×D51
SylowC3 ⋊ C5×D17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C11⋊C5×D51
commutator, cosocle, hypocenterC3×C11×C17C2×C52
FrattiniC1G
Fitting, socleC3×C5×C11×C17C2×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2805

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 36);