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C2×C5×(C13⋊C3)⋊D43 #46776512

order33540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×(C13⋊C3)⋊D43
unambiguous semidirect product(C2×C13⋊C3)⋊(C5×D43)

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, HallC13×C43 ⋊ C22×C3×C5
HallC2×C5×D559 ⋊ C3
HallC5×C13⋊C3×C43 ⋊ C22
HallC5×C13×C43 ⋊ C22×C3
HallC2×D559 ⋊ C3×C5
HallC13⋊C3×C43 ⋊ C22×C5
HallC5×C43 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ C2×D43
HallC5×C13 ⋊ C2×C3×D43
SylowC43 ⋊ C2×C5×D13⋊C3
HallC13⋊C3 ⋊ C2×C5×D43
SylowC13 ⋊ C2×C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC2×C5(C13⋊C3)⋊D43
commutator, cosocle, hypocenterC13×C43C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C13×C43C2×C3
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5590

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 132);