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C5×C29×D69 #34093402

order20010
isoclinismisoclinic class of D69
automorphism?
homologyAbelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×D69
unambiguous semidirect productC3⋊(C5×C29×D23)
unambiguous semidirect productC23⋊(C5×D3×C29)

Splittings

Fitting, socle, HallC3×C5×C23×C29 ⋊ C2
derived, HallC3×C23 ⋊ C2×C5×C29
HallC5×C23×C29 ⋊ D3
HallC3×C23×C29 ⋊ C2×C5
HallC23×C29 ⋊ C5×D3
HallC3×C5×C29 ⋊ D23
HallC3×C5×C23 ⋊ C2×C29
HallC5×C23 ⋊ D3×C29
HallC3×C29 ⋊ C5×D23
SylowC23 ⋊ C5×D3×C29
HallC3×C5 ⋊ C29×D23
SylowC3 ⋊ C5×C29×D23

Subgroups

subgroupG/H
center, hypercenterC5×C29D69
commutator, cosocle, hypocenterC3×C23C2×C5×C29
FrattiniC1G
Fitting, socleC3×C5×C23×C29C2
LCSG ▷ C3×C23
UCSC1 ◁ C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 10005

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

Conjugacy classes & character table

5220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20010, 11);