Finite Group Databasebeta

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C2×C3×C17×C11⋊C5 #19150491

order5610
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C17×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C3×C11)⋊(C5×C17)
unambiguous semidirect product(C2×C11×C17)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C11×C17)⋊C5

Splittings

Fitting, socle, HallC2×C3×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C17
HallC3×C11×C17 ⋊ C2×C5
HallC2×C11×C17 ⋊ C3×C5
HallC11×C17 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C17
HallC3×C11 ⋊ C2×C5×C17
HallC2×C11 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17C11⋊C5
commutator, hypocenterC11C2×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C11×C17C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

714 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C17×C11⋊C5, C3×C11⋊C5×Dic17, C3×C17×Dic11⋊C5, …
maximal normal subgroup ofC3×C4×C17×C11⋊C5, C3×C11⋊C5×Dic17, C3×C17×Dic11⋊C5, …
maximal quotient ofC3×C4×C17×C11⋊C5, C22×C3×C17×C11⋊C5, C2×C9×C17×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5610, 2);