Finite Group Databasebeta

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C3×C5×C11×D85 #43242533

order28050
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D85
unambiguous semidirect productC5⋊(C3×C5×C11×D17)
unambiguous semidirect productC17⋊(C3×C5×D5×C11)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derivedC5×C17 ⋊ C2×C3×C5×C11
HallC52×C11×C17 ⋊ C2×C3
HallC3×C52×C17 ⋊ C2×C11
HallC3×C52×C11 ⋊ D17
HallC3×C11×C17 ⋊ C5×D5
HallC52×C17 ⋊ C2×C3×C11
HallC52×C11 ⋊ C3×D17
HallC11×C17 ⋊ C3×C5×D5
HallC3×C52 ⋊ C11×D17
HallC3×C17 ⋊ C5×D5×C11
SylowC52 ⋊ C3×C11×D17
SylowC17 ⋊ C3×C5×D5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D85
commutator, cosocle, hypocenterC5×C17C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C3×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

7260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 58);