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D11×C41⋊C5 #17985239

order4510
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD11×C41⋊C5

Splittings

Fitting, socle, derived, HallC11×C41 ⋊ C2×C5
HallC11×C41⋊C5 ⋊ C2
HallD11×C41 ⋊ C5
SylowC41 ⋊ C5×D11
SylowC11 ⋊ C2×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C41C2×C5
LCSG ▷ C11×C41
UCSC1

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

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D11×C41⋊C5, D33×C41⋊C5, AGL(1,𝔽11)×C41⋊C5, …
maximal normal subgroup ofC3×D11×C41⋊C5, AGL(1,𝔽11)×C41⋊C5, C5×D11×C41⋊C5, …
maximal quotient ofC3×D11×C41⋊C5, D33×C41⋊C5, D11×C41⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4510, 21);