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C17×D13⋊(C52⋊C3) #45684145

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

Aliases

direct productC17×D13⋊(C52⋊C3)
unambiguous semidirect productD13⋊(C17×C52⋊C3)
unambiguous semidirect product(C17×D13)⋊(C52⋊C3)

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derived, HallC52×C13 ⋊ C2×C3×C17
HallC17×C13⋊(C52⋊C3) ⋊ C2
HallC52×C17×D13 ⋊ C3
HallC13⋊(C52⋊C3) ⋊ C2×C17
HallC52×D13 ⋊ C3×C17
HallC17×D13 ⋊ C52⋊C3
HallC52×C17 ⋊ D13⋊C3
HallC13×C17 ⋊ C2×C52⋊C3
HallD13 ⋊ C17×C52⋊C3
SylowC52 ⋊ C17×D13⋊C3
SylowC13 ⋊ C2×C17×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC17D13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C13C2×C3×C17
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C52×C13
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 27);