Finite Group Databasebeta

← Prev (#36339470) Next (#36339472) →

C3×D17×D105 #36339471

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

Aliases

direct productC3×D17×D105
unambiguous semidirect product(C3×D17)⋊(C3×D35)
unambiguous semidirect product(C5×D17)⋊(C3×D21)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C22
derivedC3×C5×C7×C17 ⋊ C22×C3
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D17
HallC32×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×C3×D15
HallC5×C17 ⋊ C2×C3×D21
HallC32×C7 ⋊ D5×D17
HallC32×C5 ⋊ D7×D17
HallC5×C7 ⋊ C3×D3×D17
SylowC17 ⋊ C2×C3×D105
SylowC32 ⋊ D17×D35
SylowC7 ⋊ C3×D15×D17
SylowC5 ⋊ C3×D17×D21

Subgroups

subgroupG/H
center, hypercenterC3D17×D105
commutator, cosocle, hypocenterC3×C5×C7×C17C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

1620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 303);