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C2×C3×C5×D539 #44568424

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D539

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC11×C49 ⋊ C22×C3×C5
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC3×C11×C49 ⋊ C22×C5
HallC3×C5×C49 ⋊ C2×D11
HallC5×C49 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C3×D49
SylowC49 ⋊ C2×C3×C5×D11
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C2×C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D539
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C2×C3×C5×D77
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C11×C49
UCSC1 ◁ C2×C3×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)(61,62,63,64,65)(66,67,68);(1,2,4,6,8,10,11,9,7,5,3)(12,26,50,60,52,30,15,18,39,56,54,43,21,24,27,48,46,44,31,34,36,40,37,35,33,32,45,47,28,25,23,22,53,55,41,19,17,16,49,59,51,29,14,13,38,57,58,42,20)(69,70)

Conjugacy classes & character table

8130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 126);