Finite Group Databasebeta

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C3×C7×D5×D19 #22547702

order7980
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC3×C7×D5×D19

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C22
derived, HallC5×C19 ⋊ C22×C3×C7
HallC5×C7×C19 ⋊ C22×C3
HallC3×C7×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C22×C7
HallC7×C19 ⋊ C2×C3×D5
HallC3×C5×C7 ⋊ C2×D19
HallC3×C19 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×C3×D19
SylowC19 ⋊ C2×C3×C7×D5
HallC3×C5 ⋊ C2×C7×D19
SylowC5 ⋊ C2×C3×C7×D19

Subgroups

subgroupG/H
center, hypercenterC3×C7D5×D19
commutator, hypocenterC5×C19C22×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C5×C19
UCSC1 ◁ C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D5×#4294⋊C2, D5×#14558780, D5×#14558781, …
maximal normal subgroup ofC7×D5×#4294⋊C2, D5×#14558780, D5×#14558781, …
maximal quotient ofC7×C9×D5×D19, C32×C7×D5×D19, C3×C7×D15×D19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 127);