Finite Group Databasebeta

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D17×D465 #44539375

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

Aliases

direct productD17×D465
unambiguous semidirect product(C3×D17)⋊D155
unambiguous semidirect product(C5×D17)⋊D93
unambiguous semidirect product(C31×D17)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C2×D3
HallC3×C17×C31 ⋊ C2×D5
HallC17×C31 ⋊ C2×D15
HallC3×C5×C31 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D31
HallC5×C31 ⋊ D3×D17
HallC3×C31 ⋊ D5×D17
HallC5×C17 ⋊ C2×D93
HallC3×C17 ⋊ C2×D155
SylowC31 ⋊ D15×D17
SylowC17 ⋊ C2×D465
HallC3×C5 ⋊ D17×D31
SylowC5 ⋊ D17×D93
SylowC3 ⋊ D17×D155

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C17×C31C22
LCSG ▷ C3×C5×C17×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 132);