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C3×D4921 #44443288

order29526
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4921

Splittings

Fitting, socle, HallC3×C7×C19×C37 ⋊ C2
derived, HallC7×C19×C37 ⋊ C2×C3
HallC3×C19×C37 ⋊ D7
HallC3×C7×C37 ⋊ D19
HallC19×C37 ⋊ C3×D7
HallC3×C7×C19 ⋊ D37
HallC7×C37 ⋊ C3×D19
HallC7×C19 ⋊ C3×D37
HallC3×C37 ⋊ D133
HallC3×C19 ⋊ D259
SylowC37 ⋊ C3×D133
HallC3×C7 ⋊ D703
SylowC19 ⋊ C3×D259
SylowC7 ⋊ C3×D703

Subgroups

subgroupG/H
center, hypercenterC3D4921
commutator, cosocle, hypocenterC7×C19×C37C2×C3
FrattiniC1G
Fitting, socleC3×C7×C19×C37C2
LCSG ▷ C7×C19×C37
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 14763

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2,3)(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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(5,10)(6,9)(7,8)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

7386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29526, 21);