Finite Group Databasebeta

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C17×D15×C11⋊C5 #43242514

order28050
automorphism?
homologyAbelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D15×C11⋊C5
unambiguous semidirect productC3⋊(D5×C17×C11⋊C5)
unambiguous semidirect productC5⋊(D3×C17×C11⋊C5)
unambiguous semidirect product(C11×D15)⋊(C5×C17)
unambiguous semidirect product(C11×C17×D15)⋊C5

Splittings

Fitting, socleC3×C5×C11×C17 ⋊ C2×C5
derivedC3×C5×C11 ⋊ C2×C5×C17
HallC3×C5×C17×C11⋊C5 ⋊ C2
HallC5×C17×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ C2×C17
HallC3×C11×C17 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D3×C17
HallC11×C17 ⋊ C5×D15
HallC3×C17 ⋊ D5×C11⋊C5
HallC3×C11 ⋊ C5×D5×C17
SylowC11 ⋊ C5×C17×D15
SylowC3 ⋊ D5×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC17D15×C11⋊C5
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C11×C17C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2805

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 39);