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C11⋊C5×D29 #15691908

order3190
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D29
unambiguous semidirect productC29⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D29)⋊C5

Splittings

Fitting, socle, derived, HallC11×C29 ⋊ C2×C5
HallC29×C11⋊C5 ⋊ C2
HallC11×D29 ⋊ C5
SylowC29 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C29C2×C5
LCSG ▷ C11×C29
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 319

A minimal faithful permutation representation — 2 generators on 40 points:

(2,3,5,8,7)(4,6,10,11,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(1,2,4,7,3,5,9,11,6,8,10)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C11⋊C5×D29, C11⋊C5×D145, C7×C11⋊C5×D29, …
maximal normal subgroup ofC5×C11⋊C5×D29, C7×C11⋊C5×D29, C11⋊C5×D29⋊C7, …
maximal quotient ofD29×C11⋊C25, C5×C11⋊C5×D29, C11⋊C5×D145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3190, 10);