Finite Group Databasebeta

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C5×C11×C17×C3⋊Dic3 #46777973

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C17 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×C17×C3⋊Dic3
unambiguous semidirect productC3⋊(C5×C11×Dic3×C17)

Splittings

derived, SylowC32 ⋊ C4×C5×C11×C17
HallC32×C5×C11×C17 ⋊ C4
HallC32×C11×C17 ⋊ C4×C5
HallC32×C5×C17 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C17
HallC32×C17 ⋊ C4×C5×C11
HallC32×C11 ⋊ C4×C5×C17
HallC32×C5 ⋊ C4×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C17C3⋊D3
commutator, hypocenterC32C4×C5×C11×C17
FrattiniC2C5×C11×C17×C3⋊D3
Fitting, socle, prime radicalC2×C32×C5×C11×C17C2
cosocleC2×C32C2×C5×C11×C17
LCSG ▷ C32
UCSC1 ◁ C2×C5×C11×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

11220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 141);