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C2×D2829 #26015235

order11316
automorphismAut(G) order 9958080
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5658
direct productC2×D2829
unambiguous semidirect product(C2×C3)⋊D943
unambiguous semidirect product(C2×C23)⋊D123
unambiguous semidirect product(C2×C41)⋊D69

Splittings

Fitting, socleC2×C3×C23×C41 ⋊ C2
derived, HallC3×C23×C41 ⋊ C22
HallC23×C41 ⋊ C2×D3
HallC3×C41 ⋊ C2×D23
HallC3×C23 ⋊ C2×D41
SylowC41 ⋊ C2×D69
SylowC23 ⋊ C2×D123
SylowC3 ⋊ C2×D943

Subgroups

subgroupG/H
center, hypercenterC2D2829
commutator, cosocle, hypocenterC3×C23×C41C22
FrattiniC1G
Fitting, socleC2×C3×C23×C41C2
LCSG ▷ C3×C23×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 5658

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

Conjugacy classes & character table

2832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D8487, D3×D2829, C2×C3×D2829, …
maximal normal subgroup ofC2×C3×D2829, D11316
maximal quotient ofC2×D8487, D3×D2829, C2×C3×D2829, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11316, 22);