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C11×D17×D39 #44415786

order29172
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D17×D39
unambiguous semidirect product(C3×D17)⋊(C11×D13)
unambiguous semidirect product(C13×D17)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C22
derived, HallC3×C13×C17 ⋊ C22×C11
HallC11×C13×C17 ⋊ C2×D3
HallC3×C11×C17 ⋊ C2×D13
HallC3×C11×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×D3×C11
HallC11×C17 ⋊ C2×D39
HallC11×C13 ⋊ D3×D17
HallC3×C17 ⋊ C2×C11×D13
HallC3×C13 ⋊ C2×C11×D17
HallC3×C11 ⋊ D13×D17
SylowC17 ⋊ C2×C11×D39
SylowC13 ⋊ D3×C11×D17
SylowC3 ⋊ C11×D13×D17

Subgroups

subgroupG/H
center, hypercenterC11D17×D39
commutator, cosocle, hypocenterC3×C13×C17C22×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C17C22
LCSG ▷ C3×C13×C17
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 78);