Finite Group Databasebeta

← Prev (#45684153) Next (#45684155) →

C13×C17×(C5⋊D5)⋊C3 #45684154

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C17 · Schur multiplier (H2) = C5

Aliases

direct productC13×C17×(C5⋊D5)⋊C3
unambiguous semidirect product(C5⋊D5)⋊(C3×C13×C17)
unambiguous semidirect product(C17×C5⋊D5)⋊(C3×C13)

Splittings

Fitting, socle, HallC52×C13×C17 ⋊ C2×C3
derived, SylowC52 ⋊ C2×C3×C13×C17
HallC13×C17×C52⋊C3 ⋊ C2
HallC13×C17×C5⋊D5 ⋊ C3
HallC17×C52⋊C3 ⋊ C2×C13
HallC13×C52⋊C3 ⋊ C2×C17
HallC17×C5⋊D5 ⋊ C3×C13
HallC13×C5⋊D5 ⋊ C3×C17
HallC52×C17 ⋊ C2×C3×C13
HallC52×C13 ⋊ C2×C3×C17
HallC52⋊C3 ⋊ C2×C13×C17
HallC5⋊D5 ⋊ C3×C13×C17

Subgroups

subgroupG/H
center, hypercenterC13×C17(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C2×C3×C13×C17
FrattiniC1G
Fitting, socleC52×C13×C17C2×C3
LCSG ▷ C52
UCSC1 ◁ C13×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 36);