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C2×D8855 #47978491

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

Aliases

dihedralD17710
direct productC2×D8855
unambiguous semidirect product(C2×C5)⋊D1771
unambiguous semidirect product(C2×C7)⋊D1265
unambiguous semidirect product(C2×C11)⋊D805
unambiguous semidirect product(C2×C23)⋊D385

Splittings

Fitting, socleC2×C5×C7×C11×C23 ⋊ C2
derived, HallC5×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C2×D5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC11×C23 ⋊ C2×D35
HallC7×C23 ⋊ C2×D55
HallC5×C23 ⋊ C2×D77
HallC7×C11 ⋊ C2×D115
HallC5×C11 ⋊ C2×D161
HallC5×C7 ⋊ C2×D253
SylowC23 ⋊ C2×D385
SylowC11 ⋊ C2×D805
SylowC7 ⋊ C2×D1265
SylowC5 ⋊ C2×D1771

Subgroups

subgroupG/H
center, hypercenterC2D8855
commutator, cosocle, hypocenterC5×C7×C11×C23C22
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C23C2
LCSG ▷ C5×C7×C11×C23
UCSC1 ◁ C2

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:

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

Conjugacy classes & character table

8858 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 125);