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C5×C11×D123 #27214262

order13530
isoclinismisoclinic class of D123
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D123
unambiguous semidirect productC3⋊(C5×C11×D41)

Splittings

Fitting, socle, HallC3×C5×C11×C41 ⋊ C2
derived, HallC3×C41 ⋊ C2×C5×C11
HallC5×C11×C41 ⋊ D3
HallC3×C11×C41 ⋊ C2×C5
HallC3×C5×C41 ⋊ C2×C11
HallC11×C41 ⋊ C5×D3
HallC5×C41 ⋊ D3×C11
HallC3×C5×C11 ⋊ D41
SylowC41 ⋊ C5×D3×C11
HallC3×C11 ⋊ C5×D41
HallC3×C5 ⋊ C11×D41
SylowC3 ⋊ C5×C11×D41

Subgroups

subgroupG/H
center, hypercenterC5×C11D123
commutator, cosocle, hypocenterC3×C41C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C41C2
LCSG ▷ C3×C41
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 6765

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

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D41, C5×D11×D123, C5×D33⋊D41, …
maximal normal subgroup ofC5×D3×C11×D41, C5×D11×D123, C5×D33⋊D41, …
maximal quotient ofC5×C11×Dic123, C2×C5×C11×D123

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13530, 16);