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C3×C7×C11⋊C5 #11923871

order1155
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C7)
unambiguous semidirect product(C3×C11)⋊(C5×C7)
unambiguous semidirect product(C3×C7×C11)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C7
HallC7×C11 ⋊ C3×C5
HallC3×C11 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7C11⋊C5
commutator, cosocle, hypocenterC11C3×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C11C5
LCSG ▷ C11
UCSC1 ◁ C3×C7

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 231

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,3)(4,5,6,7,8,9,10)(12,13,15,18,17)(14,16,20,21,19);(11,12,14,17,13,15,19,21,16,18,20)

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C7×C11⋊C5, C3×C7×AGL(1,𝔽11), C3×D7×C11⋊C5, …
maximal normal subgroup ofC2×C3×C7×C11⋊C5, C3×C7×AGL(1,𝔽11), C3×D7×C11⋊C5, …
maximal quotient ofC2×C3×C7×C11⋊C5, C7×C9×C11⋊C5, C32×C7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1155, 2);