Finite Group Databasebeta

← Prev (#22547696) Next (#22547698) →

C3×C5×D7×D19 #22547697

order7980
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×D7×D19

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C22
derived, HallC7×C19 ⋊ C22×C3×C5
HallC5×C7×C19 ⋊ C22×C3
HallC3×C7×C19 ⋊ C22×C5
HallC3×C5×C19 ⋊ C2×D7
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ C2×C3×D7
HallC3×C19 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×C3×D19
HallC3×C7 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C3×C5×D7
SylowC7 ⋊ C2×C3×C5×D19

Subgroups

subgroupG/H
center, hypercenterC3×C5D7×D19
commutator, hypocenterC7×C19C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C7×C19
UCSC1 ◁ C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

825 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#14558780⋊C2, C5×#14558781⋊C2, C5×D19×D7⋊C9, …
maximal normal subgroup ofC5×#14558780⋊C2, C5×#14558781⋊C2, C5×D19×D7⋊C9, …
maximal quotient ofC5×C9×D7×D19, C32×C5×D7×D19, C3×C5×D19×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 122);