Finite Group Databasebeta

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C3×C4×C43×C11⋊C5 #43248755

order28380
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C43×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C3×C5×C43)
unambiguous semidirect product(C3×C4×C11)⋊(C5×C43)
unambiguous semidirect product(C3×C4×C11×C43)⋊C5

Splittings

Fitting, HallC3×C4×C11×C43 ⋊ C5
derived, SylowC11 ⋊ C3×C4×C5×C43
HallC4×C11×C43 ⋊ C3×C5
HallC3×C11×C43 ⋊ C4×C5
HallC11×C43 ⋊ C3×C4×C5
HallC3×C4×C11 ⋊ C5×C43
HallC4×C11 ⋊ C3×C5×C43
HallC3×C11 ⋊ C4×C5×C43

Subgroups

subgroupG/H
center, hypercenterC3×C4×C43C11⋊C5
commutator, hypocenterC11C3×C4×C5×C43
FrattiniC2C2×C3×C43×C11⋊C5
FittingC3×C4×C11×C43C5
socleC2×C3×C11×C43C2×C5
prime radicalC2×C3×C43×C11⋊C5C2
cosocleC2×C11C2×C3×C5×C43
LCSG ▷ C11
UCSC1 ◁ C3×C4×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5676

Conjugacy classes & character table

3612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 2);