Finite Group Databasebeta

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C2×C17×C3⋊D105 #36339592

order21420
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C17×C3⋊D105
unambiguous semidirect product(C2×C3)⋊(C17×D105)
unambiguous semidirect product(C2×C5)⋊(C17×C3⋊D21)
unambiguous semidirect product(C2×C7)⋊(C17×C3⋊D15)

Splittings

Fitting, socleC2×C32×C5×C7×C17 ⋊ C2
derived, HallC32×C5×C7 ⋊ C22×C17
HallC32×C5×C7×C17 ⋊ C22
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×C3⋊D3
HallC32×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×C3⋊D15
HallC5×C17 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×D5×C17
HallC32×C5 ⋊ C2×D7×C17
HallC5×C7 ⋊ C2×C17×C3⋊D3
SylowC32 ⋊ C2×C17×D35
SylowC7 ⋊ C2×C17×C3⋊D15
SylowC5 ⋊ C2×C17×C3⋊D21

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C22×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C17C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C2×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10710

Conjugacy classes & character table

5406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 424);