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C3×D65⋊D43 #46776552

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

Aliases

direct productC3×D65⋊D43

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C22
derived, HallC5×C13×C43 ⋊ C22×C3
HallC3×C13×C43 ⋊ C2×D5
HallC3×C5×C43 ⋊ C2×D13
HallC13×C43 ⋊ C2×C3×D5
HallC5×C43 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C2×D43
HallC3×C43 ⋊ D5×D13
HallC5×C13 ⋊ C2×C3×D43
SylowC43 ⋊ C3×D5×D13
HallC3×C13 ⋊ D5×D43
HallC3×C5 ⋊ D13×D43
SylowC13 ⋊ C3×D5×D43
SylowC5 ⋊ C3×D13×D43

Subgroups

subgroupG/H
center, hypercenterC3D65⋊D43
commutator, cosocle, hypocenterC5×C13×C43C22×C3
FrattiniC1G
Fitting, socleC3×C5×C13×C43C22
LCSG ▷ C5×C13×C43
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

2238 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 172);