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C17×D483 #30655990

order16422
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D483
unambiguous semidirect productC3⋊(C17×D161)
unambiguous semidirect productC7⋊(C17×D69)
unambiguous semidirect productC23⋊(C17×D21)

Splittings

Fitting, socle, HallC3×C7×C17×C23 ⋊ C2
derived, HallC3×C7×C23 ⋊ C2×C17
HallC7×C17×C23 ⋊ D3
HallC3×C17×C23 ⋊ D7
HallC17×C23 ⋊ D21
HallC3×C7×C17 ⋊ D23
HallC7×C23 ⋊ D3×C17
HallC7×C17 ⋊ D69
HallC3×C23 ⋊ D7×C17
HallC3×C17 ⋊ D161
SylowC23 ⋊ C17×D21
HallC3×C7 ⋊ C17×D23
SylowC7 ⋊ C17×D69
SylowC3 ⋊ C17×D161

Subgroups

subgroupG/H
center, hypercenterC17D483
commutator, cosocle, hypocenterC3×C7×C23C2×C17
FrattiniC1G
Fitting, socleC3×C7×C17×C23C2
LCSG ▷ C3×C7×C23
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8211

Conjugacy classes & character table

4131 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×D21×D23, D17×D483, D391⋊D21, …
maximal normal subgroup ofC17×D21×D23, D17×D483, D391⋊D21, …
maximal quotient ofC17×Dic483, C2×C17×D483

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16422, 15);