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C11⋊C5×D327 #49112584

order35970
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D327
unambiguous semidirect productC3⋊(C11⋊C5×D109)
unambiguous semidirect productC109⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D327)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C109 ⋊ C2×C5
HallC3×C11⋊C5×C109 ⋊ C2
HallC11×D327 ⋊ C5
HallC11⋊C5×C109 ⋊ D3
HallC11×C109 ⋊ C5×D3
HallC3×C109 ⋊ C2×C11⋊C5
HallC3×C11⋊C5 ⋊ D109
SylowC109 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D109
SylowC11 ⋊ C5×D327
SylowC3 ⋊ C11⋊C5×D109

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C109C2×C5
LCSG ▷ C3×C11×C109
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3597

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 24);