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C2×C7×D1265 #47978487

order35420
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D1265
unambiguous semidirect product(C2×C5)⋊(C7×D253)
unambiguous semidirect product(C2×C11)⋊(C7×D115)
unambiguous semidirect product(C2×C23)⋊(C7×D55)

Splittings

Fitting, socleC2×C5×C7×C11×C23 ⋊ C2
derived, HallC5×C11×C23 ⋊ C22×C7
HallC5×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C2×D5
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC11×C23 ⋊ C2×C7×D5
HallC7×C23 ⋊ C2×D55
HallC5×C23 ⋊ C2×C7×D11
HallC7×C11 ⋊ C2×D115
HallC5×C11 ⋊ C2×C7×D23
HallC5×C7 ⋊ C2×D253
SylowC23 ⋊ C2×C7×D55
SylowC11 ⋊ C2×C7×D115
SylowC5 ⋊ C2×C7×D253

Subgroups

subgroupG/H
center, hypercenterC2×C7D1265
commutator, cosocle, hypocenterC5×C11×C23C22×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C23C2
LCSG ▷ C5×C11×C23
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 17710

A minimal faithful permutation representation — 2 generators on 48 points:

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

Conjugacy classes & character table

8876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 121);