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C11×D41⋊C5 #17985233

order4510
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D41⋊C5
unambiguous semidirect productD41⋊(C5×C11)
unambiguous semidirect product(C41⋊C5)⋊(C2×C11)

Splittings

Fitting, socle, HallC11×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C2×C5×C11
HallC11×C41⋊C5 ⋊ C2
HallC11×D41 ⋊ C5
HallC41⋊C5 ⋊ C2×C11
HallD41 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC11D41⋊C5
commutator, cosocle, hypocenterC41C2×C5×C11
FrattiniC1G
Fitting, socleC11×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C11

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 451

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×D41⋊C5, C11×C3⋊(D41⋊C5), C11⋊C5×D41⋊C5, …
maximal normal subgroup ofC3×C11×D41⋊C5, C11⋊C5×D41⋊C5, C5×C11×D41⋊C5, …
maximal quotient ofC3×C11×D41⋊C5, C11×C3⋊(D41⋊C5), C11×D41⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4510, 15);