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C2×D14637 #72293267

order58548
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD29274
direct productC2×D14637

Splittings

Fitting, socleC2×C3×C7×C17×C41 ⋊ C2
derived, HallC3×C7×C17×C41 ⋊ C22
HallC7×C17×C41 ⋊ C2×D3
HallC3×C17×C41 ⋊ C2×D7
HallC3×C7×C41 ⋊ C2×D17
HallC17×C41 ⋊ C2×D21
HallC3×C7×C17 ⋊ C2×D41
HallC7×C41 ⋊ C2×D51
HallC3×C41 ⋊ C2×D119
HallC7×C17 ⋊ C2×D123
HallC3×C17 ⋊ C2×D287
SylowC41 ⋊ C2×D357
HallC3×C7 ⋊ C2×D697
SylowC17 ⋊ C2×D861
SylowC7 ⋊ C2×D2091
SylowC3 ⋊ C2×D4879

Subgroups

subgroupG/H
center, hypercenterC2D14637
commutator, cosocle, hypocenterC3×C7×C17×C41C22
FrattiniC1G
Fitting, socleC2×C3×C7×C17×C41C2
LCSG ▷ C3×C7×C17×C41
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 29274

A minimal faithful permutation representation — 2 generators on 70 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);(4,5)(7,12)(8,11)(9,10)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

14640 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70), (4,5)(7,12)(8,11)(9,10)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51));