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C2×D2717 #24925888

order10868
automorphismAut(G) order 11737440
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5434
direct productC2×D2717
unambiguous semidirect product(C2×C11)⋊D247
unambiguous semidirect product(C2×C13)⋊D209
unambiguous semidirect product(C2×C19)⋊D143

Splittings

Fitting, socleC2×C11×C13×C19 ⋊ C2
derived, HallC11×C13×C19 ⋊ C22
HallC13×C19 ⋊ C2×D11
HallC11×C19 ⋊ C2×D13
HallC11×C13 ⋊ C2×D19
SylowC19 ⋊ C2×D143
SylowC13 ⋊ C2×D209
SylowC11 ⋊ C2×D247

Subgroups

subgroupG/H
center, hypercenterC2D2717
commutator, cosocle, hypocenterC11×C13×C19C22
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2
LCSG ▷ C11×C13×C19
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 5434

A minimal faithful permutation representation — 2 generators on 45 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

2720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11⋊#13093366, C2×C11⋊#13093367, C2×C11⋊((C13⋊C3)⋊D19), …
maximal normal subgroup ofC2×C11⋊#13093366, C2×C11⋊#13093367, C2×C11⋊((C13⋊C3)⋊D19), …
maximal quotient ofD3×D2717, C2×C3×D2717, C2×D8151, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10868, 21);