Finite Group Databasebeta

← Prev (#72295528) Next (#72295530) →

C2×D15105 #72295529

order60420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD30210
direct productC2×D15105

Splittings

Fitting, socleC2×C3×C5×C19×C53 ⋊ C2
derived, HallC3×C5×C19×C53 ⋊ C22
HallC5×C19×C53 ⋊ C2×D3
HallC3×C19×C53 ⋊ C2×D5
HallC19×C53 ⋊ C2×D15
HallC3×C5×C53 ⋊ C2×D19
HallC3×C5×C19 ⋊ C2×D53
HallC5×C53 ⋊ C2×D57
HallC3×C53 ⋊ C2×D95
HallC5×C19 ⋊ C2×D159
HallC3×C19 ⋊ C2×D265
SylowC53 ⋊ C2×D285
SylowC19 ⋊ C2×D795
HallC3×C5 ⋊ C2×D1007
SylowC5 ⋊ C2×D3021
SylowC3 ⋊ C2×D5035

Subgroups

subgroupG/H
center, hypercenterC2D15105
commutator, cosocle, hypocenterC3×C5×C19×C53C22
FrattiniC1G
Fitting, socleC2×C3×C5×C19×C53C2
LCSG ▷ C3×C5×C19×C53
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 82
transitive degreeμt(G) = 30210

A minimal faithful permutation representation — 2 generators on 82 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);(4,5)(7,10)(8,9)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(31,82)(32,81)(33,80)(34,79)(35,78)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Conjugacy classes & character table

15108 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), (4,5)(7,10)(8,9)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(31,82)(32,81)(33,80)(34,79)(35,78)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57));