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C2×D8827 #47977212

order35308
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17654
direct productC2×D8827
unambiguous semidirect product(C2×C7)⋊D1261
unambiguous semidirect product(C2×C13)⋊D679
unambiguous semidirect product(C2×C97)⋊D91

Splittings

Fitting, socleC2×C7×C13×C97 ⋊ C2
derived, HallC7×C13×C97 ⋊ C22
HallC13×C97 ⋊ C2×D7
HallC7×C97 ⋊ C2×D13
SylowC97 ⋊ C2×D91
HallC7×C13 ⋊ C2×D97
SylowC13 ⋊ C2×D679
SylowC7 ⋊ C2×D1261

Subgroups

subgroupG/H
center, hypercenterC2D8827
commutator, cosocle, hypocenterC7×C13×C97C22
FrattiniC1G
Fitting, socleC2×C7×C13×C97C2
LCSG ▷ C7×C13×C97
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 119
transitive degreeμt(G) = 17654

A minimal faithful permutation representation — 2 generators on 119 points:

(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(4,9)(5,8)(6,7)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,119)(25,118)(26,117)(27,116)(28,115)(29,114)(30,113)(31,112)(32,111)(33,110)(34,109)(35,108)(36,107)(37,106)(38,105)(39,104)(40,103)(41,102)(42,101)(43,100)(44,99)(45,98)(46,97)(47,96)(48,95)(49,94)(50,93)(51,92)(52,91)(53,90)(54,89)(55,88)(56,87)(57,86)(58,85)(59,84)(60,83)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,75)(69,74)(70,73)(71,72)

Conjugacy classes & character table

8830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35308, 35);