Finite Group Databasebeta

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D5×C17×C3⋊D21 #36339556

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

Aliases

direct productD5×C17×C3⋊D21
unambiguous semidirect product(C3×D5)⋊(C17×D21)
unambiguous semidirect product(C7×D5)⋊(C17×C3⋊D3)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC17D5×C3⋊D21
commutator, cosocle, hypocenterC32×C5×C7C22×C17
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C17

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 5355

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 388);