Finite Group Databasebeta

← Prev (#36339556) Next (#36339558) →

D5×C3⋊D357 #36339557

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

Aliases

direct productD5×C3⋊D357
unambiguous semidirect product(C3×D5)⋊D357
unambiguous semidirect product(C7×D5)⋊(C3⋊D51)
unambiguous semidirect product(D5×C17)⋊(C3⋊D21)

Splittings

Fitting, socle, derived, HallC32×C5×C7×C17 ⋊ C22
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D17
HallC32×C17 ⋊ D5×D7
HallC7×C17 ⋊ D5×C3⋊D3
HallC5×C17 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ D5×D17
HallC32×C5 ⋊ C2×D119
HallC5×C7 ⋊ C2×C3⋊D51
SylowC17 ⋊ D5×C3⋊D21
SylowC32 ⋊ D5×D119
SylowC7 ⋊ D5×C3⋊D51
SylowC5 ⋊ C2×C3⋊D357

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C17C22
LCSG ▷ C32×C5×C7×C17
UCSC1

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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

2148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 389);