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C2×C5×D1617 #44568432

order32340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1617
unambiguous semidirect product(C2×C3)⋊(C5×D539)
unambiguous semidirect product(C2×C49)⋊(C5×D33)

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC3×C11×C49 ⋊ C22×C5
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C2×D3
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×C5×D3
HallC5×C49 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D147
SylowC49 ⋊ C2×C5×D33
HallC3×C11 ⋊ C2×C5×D49
HallC3×C5 ⋊ C2×D539
SylowC11 ⋊ C2×C5×D147
SylowC3 ⋊ C2×C5×D539

Subgroups

subgroupG/H
center, hypercenterC2×C5D1617
commutator, cosocle, hypocenterC3×C11×C49C22×C5
FrattiniC7C2×C5×D231
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C3×C11×C49
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 16170

A minimal faithful permutation representation — 2 generators on 70 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,15)(14,18)(16,21)(17,24)(19,27)(20,26)(22,31)(23,34)(25,36)(28,40)(29,39)(30,38)(32,33)(35,45)(37,47)(41,48)(42,50)(43,49)(44,53)(46,55)(51,56)(52,57)(54,59)(58,60)(62,63)(64,65,66,67,68);(1,2,4,6,8,10,11,9,7,5,3)(12,48,23,57,43,45,29,18,37,16,60,31,55,20,27,25,38,54,32,51,15,40,17,50,44,53,42,24,28,13,56,33,59,30,36,19,26,46,22,58,21,47,14,39,35,49,52,34,41)(61,62,63)(69,70)

Conjugacy classes & character table

8100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 134);