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C11×C43⋊C7 #15693271

order3311
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C43⋊C7
unambiguous semidirect productC43⋊(C7×C11)
unambiguous semidirect product(C11×C43)⋊C7

Splittings

Fitting, socle, HallC11×C43 ⋊ C7
derived, SylowC43 ⋊ C7×C11

Subgroups

subgroupG/H
center, hypercenterC11C43⋊C7
commutator, cosocle, hypocenterC43C7×C11
FrattiniC1G
Fitting, socleC11×C43C7
LCSG ▷ C43
UCSC1 ◁ C11

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 473

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,16,20,25,33,46)(15,18,22,29,40,51,17)(19,24,31,44,21,27,36)(23,28,38,49,32,43,54)(26,35,48,45,34,30,42)(37,47,39,50,41,52,53);(12,13,15,19,16,21,28,39,22,30,43,33,31,45,35,48,25,34,47,44,36,46,51,54,49,42,53,29,41,50,52,38,40,27,37,20,26,24,32,18,23,14,17)

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C11×C43⋊C7, C11⋊C5×C43⋊C7, C7×C11×C43⋊C7, …
maximal normal subgroup ofC5×C11×C43⋊C7, C11⋊C5×C43⋊C7, C7×C11×C43⋊C7, …
maximal quotient ofC5×C11×C43⋊C7, C11×C43⋊C49, C7×C11×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3311, 1);