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C5×C17⋊(D31⋊C3) #30629048

order15810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17⋊(D31⋊C3)
unambiguous semidirect productC17⋊(C5×D31⋊C3)
unambiguous semidirect product(C5×D527)⋊C3

Splittings

Fitting, socle, HallC5×C17×C31 ⋊ C2×C3
derived, HallC17×C31 ⋊ C2×C3×C5
HallC5×C17×C31⋊C3 ⋊ C2
HallC5×D527 ⋊ C3
HallC17×C31⋊C3 ⋊ C2×C5
HallD527 ⋊ C3×C5
HallC5×C31⋊C3 ⋊ D17
HallC5×C31 ⋊ C3×D17
HallC31⋊C3 ⋊ C5×D17
HallC5×C17 ⋊ D31⋊C3
SylowC31 ⋊ C3×C5×D17
SylowC17 ⋊ C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C17⋊(D31⋊C3)
commutator, cosocle, hypocenterC17×C31C2×C3×C5
FrattiniC1G
Fitting, socleC5×C17×C31C2×C3
LCSG ▷ C17×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2635

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D17×D31⋊C3, D5×C17⋊(D31⋊C3), D85⋊(D31⋊C3), …
maximal normal subgroup ofC5×D17×D31⋊C3, D5×C17⋊(D31⋊C3), D85⋊(D31⋊C3), …
maximal quotient ofC5×(C31⋊C3)⋊Dic17, C2×C5×C17⋊(D31⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 29);