Finite Group Databasebeta

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C2×C17×D465 #44539409

order31620
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D465
unambiguous semidirect product(C2×C3)⋊(C17×D155)
unambiguous semidirect product(C2×C5)⋊(C17×D93)
unambiguous semidirect product(C2×C31)⋊(C17×D15)

Splittings

Fitting, socleC2×C3×C5×C17×C31 ⋊ C2
derived, HallC3×C5×C31 ⋊ C22×C17
HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C2×D3
HallC3×C17×C31 ⋊ C2×D5
HallC17×C31 ⋊ C2×D15
HallC3×C5×C17 ⋊ C2×D31
HallC5×C31 ⋊ C2×D3×C17
HallC3×C31 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×D93
HallC3×C17 ⋊ C2×D155
SylowC31 ⋊ C2×C17×D15
HallC3×C5 ⋊ C2×C17×D31
SylowC5 ⋊ C2×C17×D93
SylowC3 ⋊ C2×C17×D155

Subgroups

subgroupG/H
center, hypercenterC2×C17D465
commutator, cosocle, hypocenterC3×C5×C31C22×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C3×C5×C31
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15810

Conjugacy classes & character table

7956 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 166);