Finite Group Databasebeta

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C2×C5⋊(C17⋊(D31⋊C3)) #44539332

order31620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(C17⋊(D31⋊C3))
unambiguous semidirect product(C2×C5)⋊(C17⋊(D31⋊C3))
unambiguous semidirect product(C2×C17)⋊(C5⋊(D31⋊C3))
unambiguous semidirect product(C2×C31⋊C3)⋊D85
unambiguous semidirect product(C2×D2635)⋊C3

Splittings

Fitting, socleC2×C5×C17×C31 ⋊ C2×C3
derived, HallC5×C17×C31 ⋊ C22×C3
HallC2×D2635 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C22
HallC17×C31⋊C3 ⋊ C2×D5
HallC17×C31 ⋊ C2×C3×D5
HallC5×C31⋊C3 ⋊ C2×D17
HallC5×C31 ⋊ C2×C3×D17
HallC31⋊C3 ⋊ C2×D85
HallC5×C17 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C3×D85
SylowC17 ⋊ C2×C5⋊(D31⋊C3)
SylowC5 ⋊ C2×C17⋊(D31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C17⋊(D31⋊C3))
commutator, cosocle, hypocenterC5×C17×C31C22×C3
FrattiniC1G
Fitting, socleC2×C5×C17×C31C2×C3
LCSG ▷ C5×C17×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5270

Conjugacy classes & character table

1114 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 89);