Finite Group Databasebeta

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C17×#157×C11⋊C5 #46777993

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

Aliases

direct productC17×#157×C11⋊C5
unambiguous semidirect product(C11×#157)⋊(C5×C17)
unambiguous semidirect product(C11×C17×#157)⋊C5

Splittings

Fitting, socle, HallC32×C11×C17 ⋊ C4×C5
derived, HallC32×C11 ⋊ C4×C5×C17
HallC32×C17×C11⋊C5 ⋊ C4
HallC11×C17×#157 ⋊ C5
HallC32×C11⋊C5 ⋊ C4×C17
HallC11×#157 ⋊ C5×C17
HallC11×C17 ⋊ C5×#157
HallC32×C17 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×C17×#157
SylowC32 ⋊ C4×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC17#157×C11⋊C5
commutator, hypocenterC32×C11C4×C5×C17
FrattiniC1G
Fitting, socleC32×C11×C17C4×C5
prime radicalC17×C3⋊D3×C11⋊C5C2
cosocleC11×C3⋊D3C2×C5×C17
LCSG ▷ C32×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1122

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 161);