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C17×C5⋊(D31⋊C3) #30629050

order15810
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C5⋊(D31⋊C3)
unambiguous semidirect productC5⋊(C17×D31⋊C3)
unambiguous semidirect product(C31⋊C3)⋊(D5×C17)
unambiguous semidirect productD155⋊(C3×C17)
unambiguous semidirect product(C17×D155)⋊C3

Splittings

Fitting, socle, HallC5×C17×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C3×C17
HallC5×C17×C31⋊C3 ⋊ C2
HallC17×D155 ⋊ C3
HallC17×C31⋊C3 ⋊ D5
HallC17×C31 ⋊ C3×D5
HallC5×C31⋊C3 ⋊ C2×C17
HallD155 ⋊ C3×C17
HallC31⋊C3 ⋊ D5×C17
HallC5×C17 ⋊ D31⋊C3
SylowC31 ⋊ C3×D5×C17
SylowC5 ⋊ C17×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C3×C17
FrattiniC1G
Fitting, socleC5×C17×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2635

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×C17×D31⋊C3, D17×C5⋊(D31⋊C3), D85⋊(D31⋊C3), …
maximal normal subgroup ofD5×C17×D31⋊C3, D17×C5⋊(D31⋊C3), D85⋊(D31⋊C3), …
maximal quotient ofC17×(C31⋊C3)⋊Dic5, C2×C17×C5⋊(D31⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 31);