Finite Group Databasebeta

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D3×D17×C121 #37590568

order24684
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productD3×D17×C121
unambiguous semidirect product(D3×C17)⋊(C2×C121)
unambiguous semidirect product(C3×D17)⋊(C2×C121)
unambiguous semidirect productD51⋊(C2×C121)

Splittings

Fitting, HallC3×C17×C121 ⋊ C22
derived, HallC3×C17 ⋊ C22×C121
HallC17×C121 ⋊ C2×D3
HallC3×C121 ⋊ C2×D17
SylowC17 ⋊ C2×D3×C121
SylowC3 ⋊ C2×D17×C121

Subgroups

subgroupG/H
center, hypercenterC121D3×D17
commutator, hypocenterC3×C17C22×C121
FrattiniC11D3×C11×D17
FittingC3×C17×C121C22
socle, cosocleC3×C11×C17C22×C11
prime radicalD3×C11×D17C11
LCSG ▷ C3×C17
UCSC1 ◁ C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6171

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 14);