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C2×D14145 #72291673

order56580
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD28290
direct productC2×D14145

Splittings

Fitting, socleC2×C3×C5×C23×C41 ⋊ C2
derived, HallC3×C5×C23×C41 ⋊ C22
HallC5×C23×C41 ⋊ C2×D3
HallC3×C23×C41 ⋊ C2×D5
HallC23×C41 ⋊ C2×D15
HallC3×C5×C41 ⋊ C2×D23
HallC3×C5×C23 ⋊ C2×D41
HallC5×C41 ⋊ C2×D69
HallC3×C41 ⋊ C2×D115
HallC5×C23 ⋊ C2×D123
HallC3×C23 ⋊ C2×D205
SylowC41 ⋊ C2×D345
SylowC23 ⋊ C2×D615
HallC3×C5 ⋊ C2×D943
SylowC5 ⋊ C2×D2829
SylowC3 ⋊ C2×D4715

Subgroups

subgroupG/H
center, hypercenterC2D14145
commutator, cosocle, hypocenterC3×C5×C23×C41C22
FrattiniC1G
Fitting, socleC2×C3×C5×C23×C41C2
LCSG ▷ C3×C5×C23×C41
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 74
transitive degreeμt(G) = 28290

A minimal faithful permutation representation — 2 generators on 74 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);(4,5)(7,10)(8,9)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)

Conjugacy classes & character table

14148 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)(34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74), (4,5)(7,10)(8,9)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55));