Finite Group Databasebeta

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C3×C5×C17×D55 #43242534

order28050
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C17×D55
unambiguous semidirect productC5⋊(C3×C5×C17×D11)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derivedC5×C11 ⋊ C2×C3×C5×C17
HallC52×C11×C17 ⋊ C2×C3
HallC3×C52×C17 ⋊ D11
HallC3×C52×C11 ⋊ C2×C17
HallC3×C11×C17 ⋊ C5×D5
HallC52×C17 ⋊ C3×D11
HallC52×C11 ⋊ C2×C3×C17
HallC11×C17 ⋊ C3×C5×D5
HallC3×C52 ⋊ C17×D11
HallC3×C11 ⋊ C5×D5×C17
SylowC52 ⋊ C3×C17×D11
SylowC11 ⋊ C3×C5×D5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17D55
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C17
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C5×C11
UCSC1 ◁ C3×C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

7395 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 59);