Finite Group Databasebeta

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C3×C11×A4×C13 #19104241

order5148
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C11×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C11×A4×C13
unambiguous semidirect productC22⋊(C32×C11×C13)
unambiguous semidirect product(C22×C3)⋊(C3×C11×C13)
unambiguous semidirect product(C22×C11)⋊(C32×C13)
unambiguous semidirect product(C22×C3×C11)⋊(C3×C13)

Splittings

Fitting, socleC22×C3×C11×C13 ⋊ C3
derived, SylowC22 ⋊ C32×C11×C13
HallC22×C11×C13 ⋊ C32
HallC22×C13 ⋊ C32×C11
HallC22×C11 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13A4
commutator, hypocenterC22C32×C11×C13
FrattiniC1G
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C22
UCSC1 ◁ C3×C11×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×A4×C13×C11⋊C5, C3×C5×C11×A4×C13, C3×C11×C13×A5, …
maximal normal subgroup ofC3×A4×C13×C11⋊C5, C3×C5×C11×A4×C13, C3×C7×C11×A4×C13
maximal quotient ofC3×C5×C11×A4×C13, C11×A4×C13×ΓL(1,𝔽8), C3×C7×C11×A4×C13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 117);