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C11⋊C5×C3⋊Dic51 #46777964

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

Aliases

direct productC11⋊C5×C3⋊Dic51
unambiguous semidirect productC3⋊(C11⋊C5×Dic51)
unambiguous semidirect product(C11×C3⋊Dic51)⋊C5

Splittings

derived, HallC32×C11×C17 ⋊ C4×C5
HallC32×C17×C11⋊C5 ⋊ C4
HallC11×C3⋊Dic51 ⋊ C5
HallC17×C11⋊C5 ⋊ C3⋊Dic3
HallC32×C11⋊C5 ⋊ Dic17
HallC11×C17 ⋊ C5×C3⋊Dic3
HallC32×C17 ⋊ C4×C11⋊C5
HallC32×C11 ⋊ C5×Dic17
SylowC17 ⋊ C3⋊Dic3×C11⋊C5
SylowC11 ⋊ C5×C3⋊Dic51
SylowC32 ⋊ C11⋊C5×Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×C3⋊D51
commutator, hypocenterC32×C11×C17C4×C5
Fitting, socle, cosocleC2×C32×C11×C17C2×C5
prime radicalC2×C32×C17×C11⋊C5C2
LCSG ▷ C32×C11×C17
UCSC1 ◁ C2

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6732

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 132);