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C2×C11×D735 #44568435

order32340
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D735
unambiguous semidirect product(C2×C3)⋊(C11×D245)
unambiguous semidirect product(C2×C5)⋊(C11×D147)
unambiguous semidirect product(C2×C49)⋊(C11×D15)

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC3×C5×C49 ⋊ C22×C11
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C2×D5
HallC11×C49 ⋊ C2×D15
HallC5×C49 ⋊ C2×D3×C11
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×D147
SylowC49 ⋊ C2×C11×D15
HallC3×C11 ⋊ C2×D245
HallC3×C5 ⋊ C2×C11×D49
SylowC5 ⋊ C2×C11×D147
SylowC3 ⋊ C2×C11×D245

Subgroups

subgroupG/H
center, hypercenterC2×C11D735
commutator, cosocle, hypocenterC3×C5×C49C22×C11
FrattiniC7C2×C11×D105
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C2×C11

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:

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

Conjugacy classes & character table

8118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 137);