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C2×C11×C19×D15 #27160097

order12540
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C22×C11×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C19×D15
unambiguous semidirect product(C2×C3)⋊(D5×C11×C19)
unambiguous semidirect product(C2×C5)⋊(D3×C11×C19)

Splittings

Fitting, socleC2×C3×C5×C11×C19 ⋊ C2
derived, HallC3×C5 ⋊ C22×C11×C19
HallC3×C5×C11×C19 ⋊ C22
HallC5×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C22×C11
HallC3×C5×C11 ⋊ C22×C19
HallC5×C19 ⋊ C2×D3×C11
HallC3×C19 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×D3×C19
HallC3×C11 ⋊ C2×D5×C19
SylowC5 ⋊ C2×D3×C11×C19
SylowC3 ⋊ C2×D5×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19D15
commutator, cosocle, hypocenterC3×C5C22×C11×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C19C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C19×D45, C2×C11×D15×C19⋊C3, D3×C11×C19×D15, …
maximal normal subgroup ofC2×C11×D15×C19⋊C3, C2×C3×C11×C19×D15
maximal quotient ofC2×C11×C19×D45, D3×C11×C19×D15, C2×C3×C11×C19×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 127);