Finite Group Databasebeta

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C3×A4×C191⋊C5 #46806010

order34380
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C191⋊C5
unambiguous semidirect productC22⋊(C32×C191⋊C5)
unambiguous semidirect product(C22×C3)⋊(C3×C191⋊C5)
unambiguous semidirect productC191⋊(C3×C5×A4)
unambiguous semidirect product(C3×C191)⋊(C5×A4)
unambiguous semidirect product(A4×C191)⋊(C3×C5)
unambiguous semidirect product(C22×C191⋊C5)⋊C32
unambiguous semidirect product(C3×A4×C191)⋊C5
unambiguous semidirect product(C22×C3×C191⋊C5)⋊C3

Splittings

Fitting, socleC22×C3×C191 ⋊ C3×C5
derived, HallC22×C191 ⋊ C32×C5
HallC3×A4×C191 ⋊ C5
HallC22×C191⋊C5 ⋊ C32
SylowC191 ⋊ C3×C5×A4
SylowC22 ⋊ C32×C191⋊C5

Subgroups

subgroupG/H
center, hypercenterC3A4×C191⋊C5
commutator, cosocle, hypocenterC22×C191C32×C5
FrattiniC1G
Fitting, socleC22×C3×C191C3×C5
LCSG ▷ C22×C191
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2292

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34380, 65);