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C3×C4×C11⋊C5 #10620334

order660
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC3×C4×C11 ⋊ C5
derived, SylowC11 ⋊ C3×C4×C5
HallC4×C11 ⋊ C3×C5
HallC3×C11 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4C11⋊C5
commutator, hypocenterC11C3×C4×C5
FrattiniC2C2×C3×C11⋊C5
FittingC3×C4×C11C5
socleC2×C3×C11C2×C5
prime radicalC2×C3×C11⋊C5C2
cosocleC2×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3)(4,5,6,7)(9,10,12,15,14)(11,13,17,18,16);(8,9,11,14,10,12,16,18,13,15,17)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C11⋊C5)⋊C8, C3⋊C8×C11⋊C5, C3⋊((C11⋊C5)⋊C8), …
maximal normal subgroup ofC3×(C11⋊C5)⋊C8, C3⋊C8×C11⋊C5, C3⋊((C11⋊C5)⋊C8), …
maximal quotient ofC3×C8×C11⋊C5, C2×C3×C4×C11⋊C5, C4×C9×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(660, 4);