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C5×D5×C17×C13⋊C3 #45684167

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

Aliases

direct productC5×D5×C17×C13⋊C3
unambiguous semidirect productC5⋊(C2×C5×C17×C13⋊C3)
unambiguous semidirect product(D5×C13)⋊(C3×C5×C17)
unambiguous semidirect product(C5×D5×C13)⋊(C3×C17)
unambiguous semidirect product(D5×C13×C17)⋊(C3×C5)
unambiguous semidirect product(C5×D5×C13×C17)⋊C3

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derivedC5×C13 ⋊ C2×C3×C5×C17
HallC52×C17×C13⋊C3 ⋊ C2
HallC5×D5×C13×C17 ⋊ C3
HallC52×C13⋊C3 ⋊ C2×C17
HallC5×D5×C13 ⋊ C3×C17
HallC52×C17 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C2×C3×C17
HallC13×C17 ⋊ C3×C5×D5
SylowC52 ⋊ C2×C17×C13⋊C3
SylowC13 ⋊ C3×C5×D5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17D5×C13⋊C3
commutator, cosocle, hypocenterC5×C13C2×C3×C5×C17
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2210

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 49);