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C11×D61⋊C3 #16860901

order4026
isoclinismisoclinic class of D61⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D61⋊C3
unambiguous semidirect productD61⋊(C3×C11)
unambiguous semidirect product(C61⋊C3)⋊(C2×C11)
unambiguous semidirect product(C11×D61)⋊C3

Splittings

Fitting, socle, HallC11×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C2×C3×C11
HallC11×C61⋊C3 ⋊ C2
HallC11×D61 ⋊ C3
HallC61⋊C3 ⋊ C2×C11
HallD61 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC11D61⋊C3
commutator, cosocle, hypocenterC61C2×C3×C11
FrattiniC1G
Fitting, socleC11×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C11

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 72
transitive degreeμt(G) = 671

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,17,18,14,15,19)(16,25,26,20,21,35)(22,38,39,28,29,51)(23,37,33,31,27,24)(30,56,57,41,42,67)(32,54,55,43,40,48)(34,36,53,45,46,49)(44,69,70,59,58,65)(47,52,68,61,60,66)(50,72,71,63,64,62);(12,13,16,22,30,42,58,64,66,67,61,45,33,18,17,23,32,44,60,29,40,49,51,65,71,55,26,37,25,36,50,63,46,21,27,35,48,62,70,39,53,54,38,52,59,43,31,15,19,24,34,47,57,68,72,69,56,41,28,20,14)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×D61⋊C3, C11×C3⋊(D61⋊C3), C5×C11×D61⋊C3, …
maximal normal subgroup ofC3×C11×D61⋊C3, C5×C11×D61⋊C3, C11×(D61⋊C3)⋊C5, …
maximal quotient ofC11×D61⋊C9, C3×C11×D61⋊C3, C11×C3⋊(D61⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4026, 10);