Finite Group Databasebeta

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C7×C17×(C3⋊D3)⋊D5 #36339518

order21420
automorphism?
homologyAbelianization (H1) = C22×C7×C17 · Schur multiplier (H2) = C2

Aliases

direct productC7×C17×(C3⋊D3)⋊D5
unambiguous semidirect product(C3⋊D3)⋊(C7×D5×C17)
unambiguous semidirect productD15⋊(D3×C7×C17)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C22
derived, HallC32×C5 ⋊ C22×C7×C17
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C22×C7
HallC5×C7×C17 ⋊ D32
HallC32×C5×C7 ⋊ C22×C17
HallC32×C17 ⋊ C2×C7×D5
HallC5×C17 ⋊ D32×C7
HallC32×C7 ⋊ C2×D5×C17
HallC5×C7 ⋊ D32×C17
SylowC32 ⋊ C2×C7×D5×C17
SylowC5 ⋊ D32×C7×C17

Subgroups

subgroupG/H
center, hypercenterC7×C17(C3⋊D3)⋊D5
commutator, cosocle, hypocenterC32×C5C22×C7×C17
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C32×C5
UCSC1 ◁ C7×C17

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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

2499 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 350);