Finite Group Databasebeta

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C3×C11×D85 #19150496

order5610
isoclinismisoclinic class of D85
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D85
unambiguous semidirect productC5⋊(C3×C11×D17)
unambiguous semidirect productC17⋊(C3×D5×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C2
derived, HallC5×C17 ⋊ C2×C3×C11
HallC5×C11×C17 ⋊ C2×C3
HallC3×C11×C17 ⋊ D5
HallC3×C5×C17 ⋊ C2×C11
HallC11×C17 ⋊ C3×D5
HallC3×C5×C11 ⋊ D17
HallC5×C11 ⋊ C3×D17
HallC3×C17 ⋊ D5×C11
SylowC17 ⋊ C3×D5×C11
HallC3×C5 ⋊ C11×D17
SylowC5 ⋊ C3×C11×D17

Subgroups

subgroupG/H
center, hypercenterC3×C11D85
commutator, hypocenterC5×C17C2×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×#66775, C3×C11×#66776, C3×C11⋊#66775, …
maximal normal subgroup ofC3×C11×#66775, C3×C11×#66776, C3×C11⋊#66775, …
maximal quotient ofC3×C11×Dic85, C2×C3×C11×D85, C9×C11×D85, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5610, 7);