Finite Group Databasebeta

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C3×C5×D209 #20262437

order6270
isoclinismisoclinic class of D209
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D209

Splittings

Fitting, socle, HallC3×C5×C11×C19 ⋊ C2
derived, HallC11×C19 ⋊ C2×C3×C5
HallC5×C11×C19 ⋊ C2×C3
HallC3×C11×C19 ⋊ C2×C5
HallC3×C5×C19 ⋊ D11
HallC3×C5×C11 ⋊ D19
HallC5×C19 ⋊ C3×D11
HallC3×C19 ⋊ C5×D11
HallC5×C11 ⋊ C3×D19
HallC3×C11 ⋊ C5×D19
SylowC19 ⋊ C3×C5×D11
SylowC11 ⋊ C3×C5×D19

Subgroups

subgroupG/H
center, hypercenterC3×C5D209
commutator, hypocenterC11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2
LCSG ▷ C11×C19
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1590 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D11×D19, C3×D5×D209, C3×D55⋊D19, …
maximal normal subgroup ofC3×C5×D11×D19, C3×D5×D209, C3×D55⋊D19, …
maximal quotient ofC3×C5×Dic209, C2×C3×C5×D209, C5×C9×D209, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6270, 7);