Finite Group Databasebeta

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C3×C11⋊C5×C169 #42124193

order27885
automorphism?
homologyAbelianization (H1) = C3×C5×C169 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×C169
unambiguous semidirect productC11⋊(C3×C5×C169)
unambiguous semidirect product(C3×C11)⋊(C5×C169)
unambiguous semidirect product(C3×C11×C169)⋊C5

Splittings

Fitting, HallC3×C11×C169 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C169
HallC11×C169 ⋊ C3×C5
HallC3×C11 ⋊ C5×C169

Subgroups

subgroupG/H
center, hypercenterC3×C169C11⋊C5
commutator, hypocenterC11C3×C5×C169
FrattiniC13C3×C13×C11⋊C5
FittingC3×C11×C169C5
socleC3×C11×C13C5×C13
prime radicalC3×C13×C11⋊C5C13
cosocleC11×C13C3×C5×C13
LCSG ▷ C11
UCSC1 ◁ C3×C169

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5577

Conjugacy classes & character table

3549 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27885, 2);