Finite Group Databasebeta

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C11×D15×C49 #30633471

order16170
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC11×D15×C49
unambiguous semidirect productC3⋊(D5×C11×C49)
unambiguous semidirect productC5⋊(D3×C11×C49)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC3×C5 ⋊ C2×C11×C49
HallC5×C11×C49 ⋊ D3
HallC3×C11×C49 ⋊ D5
HallC3×C5×C49 ⋊ C2×C11
HallC5×C49 ⋊ D3×C11
HallC3×C5×C11 ⋊ C2×C49
HallC3×C49 ⋊ D5×C11
HallC5×C11 ⋊ D3×C49
HallC3×C11 ⋊ D5×C49
SylowC5 ⋊ D3×C11×C49
SylowC3 ⋊ D5×C11×C49

Subgroups

subgroupG/H
center, hypercenterC11×C49D15
commutator, hypocenterC3×C5C2×C11×C49
FrattiniC7C7×C11×D15
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11C2×C7
prime radicalC7×C11×D15C7
cosocleC3×C5×C7C2×C7×C11
LCSG ▷ C3×C5
UCSC1 ◁ C11×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×D15×C49, C11×D15×D49, D15×D539, …
maximal normal subgroup ofD11×D15×C49, C11×D15×D49, D15×D539, …
maximal quotient ofC11×C49×Dic15, C2×C11×D15×C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 16);