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C3×Dic11⋊C5 #10620331

order660
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic11⋊C5
unambiguous semidirect productDic11⋊(C3×C5)
unambiguous semidirect product(C11⋊C5)⋊(C3×C4)
unambiguous semidirect product(C3×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C4×C5
HallC3×C11⋊C5 ⋊ C4
HallC3×Dic11 ⋊ C5
HallC11⋊C5 ⋊ C3×C4
HallDic11 ⋊ C3×C5
HallC3×C11 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽11)
commutator, hypocenterC11C3×C4×C5
FrattiniC2C3×AGL(1,𝔽11)
Fitting, socleC2×C3×C11C2×C5
prime radicalC2×C3×C11⋊C5C2
cosocleC2×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×Dic11⋊C5, (D33⋊C4)⋊C5, #63142⋊C5, …
maximal normal subgroup ofD3×Dic11⋊C5, (D33⋊C4)⋊C5, #63142⋊C5, …
maximal quotient ofC3×(C11⋊C5)⋊C8, C2×C3×Dic11⋊C5, C9×Dic11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(660, 1);