Finite Group Databasebeta

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C3×C5×C17×D65 #45684181

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C17×D65
unambiguous semidirect productC5⋊(C3×C5×C17×D13)

Splittings

Fitting, socle, HallC3×C52×C13×C17 ⋊ C2
derivedC5×C13 ⋊ C2×C3×C5×C17
HallC52×C13×C17 ⋊ C2×C3
HallC3×C52×C17 ⋊ D13
HallC3×C52×C13 ⋊ C2×C17
HallC3×C13×C17 ⋊ C5×D5
HallC52×C17 ⋊ C3×D13
HallC52×C13 ⋊ C2×C3×C17
HallC13×C17 ⋊ C3×C5×D5
HallC3×C52 ⋊ C17×D13
HallC3×C13 ⋊ C5×D5×C17
SylowC52 ⋊ C3×C17×D13
SylowC13 ⋊ C3×C5×D5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17D65
commutator, cosocle, hypocenterC5×C13C2×C3×C5×C17
FrattiniC1G
Fitting, socleC3×C52×C13×C17C2
LCSG ▷ C5×C13
UCSC1 ◁ C3×C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

Conjugacy classes & character table

8670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 63);