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C2×D15873 #72301682

order63492
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD31746
direct productC2×D15873

Splittings

Fitting, socleC2×C3×C11×C13×C37 ⋊ C2
derived, HallC3×C11×C13×C37 ⋊ C22
HallC11×C13×C37 ⋊ C2×D3
HallC3×C13×C37 ⋊ C2×D11
HallC3×C11×C37 ⋊ C2×D13
HallC13×C37 ⋊ C2×D33
HallC3×C11×C13 ⋊ C2×D37
HallC11×C37 ⋊ C2×D39
HallC11×C13 ⋊ C2×D111
HallC3×C37 ⋊ C2×D143
HallC3×C13 ⋊ C2×D407
SylowC37 ⋊ C2×D429
HallC3×C11 ⋊ C2×D481
SylowC13 ⋊ C2×D1221
SylowC11 ⋊ C2×D1443
SylowC3 ⋊ C2×D5291

Subgroups

subgroupG/H
center, hypercenterC2D15873
commutator, cosocle, hypocenterC3×C11×C13×C37C22
FrattiniC1G
Fitting, socleC2×C3×C11×C13×C37C2
LCSG ▷ C3×C11×C13×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 31746

A minimal faithful permutation representation — 2 generators on 66 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);(4,5)(7,16)(8,15)(9,14)(10,13)(11,12)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

15876 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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), (4,5)(7,16)(8,15)(9,14)(10,13)(11,12)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49));