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C2×D13845 #72291002

order55380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD27690
direct productC2×D13845

Splittings

Fitting, socleC2×C3×C5×C13×C71 ⋊ C2
derived, HallC3×C5×C13×C71 ⋊ C22
HallC5×C13×C71 ⋊ C2×D3
HallC3×C13×C71 ⋊ C2×D5
HallC3×C5×C71 ⋊ C2×D13
HallC13×C71 ⋊ C2×D15
HallC5×C71 ⋊ C2×D39
HallC3×C71 ⋊ C2×D65
HallC3×C5×C13 ⋊ C2×D71
SylowC71 ⋊ C2×D195
HallC5×C13 ⋊ C2×D213
HallC3×C13 ⋊ C2×D355
HallC3×C5 ⋊ C2×D923
SylowC13 ⋊ C2×D1065
SylowC5 ⋊ C2×D2769
SylowC3 ⋊ C2×D4615

Subgroups

subgroupG/H
center, hypercenterC2D13845
commutator, cosocle, hypocenterC3×C5×C13×C71C22
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C71C2
LCSG ▷ C3×C5×C13×C71
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 94
transitive degreeμt(G) = 27690

A minimal faithful permutation representation — 2 generators on 94 points:

(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94);(4,5)(7,10)(8,9)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(25,94)(26,93)(27,92)(28,91)(29,90)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

13848 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)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94), (4,5)(7,10)(8,9)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(25,94)(26,93)(27,92)(28,91)(29,90)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60));