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C5×C49×C11⋊C5 #27212474

order13475
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C52×C49 · Schur multiplier (H2) = C5

Aliases

direct productC5×C49×C11⋊C5
unambiguous semidirect productC11⋊(C52×C49)
unambiguous semidirect product(C5×C11)⋊(C5×C49)
unambiguous semidirect product(C11×C49)⋊C52
unambiguous semidirect product(C5×C11×C49)⋊C5

Splittings

FittingC5×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C52×C49
HallC11×C49 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C49C11⋊C5
commutator, hypocenterC11C52×C49
FrattiniC7C5×C7×C11⋊C5
FittingC5×C11×C49C5
socleC5×C7×C11C5×C7
prime radicalC5×C7×C11⋊C5C7
cosocleC7×C11C52×C7
LCSG ▷ C11
UCSC1 ◁ C5×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 2695

A minimal faithful permutation representation — 2 generators on 65 points:

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

Conjugacy classes & character table

1715 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C49×AGL(1,𝔽11), C5×C49⋊AGL(1,𝔽11), C5×C11⋊C5×D49, …
maximal normal subgroup ofC5×C49×AGL(1,𝔽11), C5×C49⋊AGL(1,𝔽11), C5×C11⋊C5×D49, …
maximal quotient ofC2×C5×C49×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13475, 4);