Finite Group Databasebeta

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C2×C13×C29×D15 #36383243

order22620
automorphism?
homologyAbelianization (H1) = C22×C13×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×C29×D15
unambiguous semidirect product(C2×C3)⋊(D5×C13×C29)
unambiguous semidirect product(C2×C5)⋊(D3×C13×C29)

Splittings

Fitting, socleC2×C3×C5×C13×C29 ⋊ C2
derived, HallC3×C5 ⋊ C22×C13×C29
HallC3×C5×C13×C29 ⋊ C22
HallC5×C13×C29 ⋊ C2×D3
HallC3×C13×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C22×C13
HallC3×C5×C13 ⋊ C22×C29
HallC5×C29 ⋊ C2×D3×C13
HallC3×C29 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×D3×C29
HallC3×C13 ⋊ C2×D5×C29
SylowC5 ⋊ C2×D3×C13×C29
SylowC3 ⋊ C2×D5×C13×C29

Subgroups

subgroupG/H
center, hypercenterC2×C13×C29D15
commutator, cosocle, hypocenterC3×C5C22×C13×C29
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C29C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C13×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11310

Conjugacy classes & character table

6786 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 173);