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C11×D609 #27211525

order13398
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D609
unambiguous semidirect productC3⋊(C11×D203)
unambiguous semidirect productC7⋊(C11×D87)
unambiguous semidirect productC29⋊(C11×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, HallC3×C7×C29 ⋊ C2×C11
HallC7×C11×C29 ⋊ D3
HallC3×C11×C29 ⋊ D7
HallC11×C29 ⋊ D21
HallC3×C7×C11 ⋊ D29
HallC7×C29 ⋊ D3×C11
HallC3×C29 ⋊ C11×D7
HallC7×C11 ⋊ D87
HallC3×C11 ⋊ D203
SylowC29 ⋊ C11×D21
HallC3×C7 ⋊ C11×D29
SylowC7 ⋊ C11×D87
SylowC3 ⋊ C11×D203

Subgroups

subgroupG/H
center, hypercenterC11D609
commutator, cosocle, hypocenterC3×C7×C29C2×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C3×C7×C29
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 6699

A minimal faithful permutation representation — 2 generators on 50 points:

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

Conjugacy classes & character table

3366 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D21×D29, D11×D609, D319⋊D21, …
maximal normal subgroup ofC11×D21×D29, D11×D609, D319⋊D21, …
maximal quotient ofC11×Dic609, C2×C11×D609

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 16);