Finite Group Databasebeta

← Prev (#44447287) Next (#44447289) →

C2×D7455 #44447288

order29820
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD14910
direct productC2×D7455
unambiguous semidirect product(C2×C3)⋊D2485
unambiguous semidirect product(C2×C5)⋊D1491
unambiguous semidirect product(C2×C7)⋊D1065
unambiguous semidirect product(C2×C71)⋊D105

Splittings

Fitting, socleC2×C3×C5×C7×C71 ⋊ C2
derived, HallC3×C5×C7×C71 ⋊ C22
HallC5×C7×C71 ⋊ C2×D3
HallC3×C7×C71 ⋊ C2×D5
HallC3×C5×C71 ⋊ C2×D7
HallC7×C71 ⋊ C2×D15
HallC5×C71 ⋊ C2×D21
HallC3×C71 ⋊ C2×D35
HallC3×C5×C7 ⋊ C2×D71
SylowC71 ⋊ C2×D105
HallC5×C7 ⋊ C2×D213
HallC3×C7 ⋊ C2×D355
HallC3×C5 ⋊ C2×D497
SylowC7 ⋊ C2×D1065
SylowC5 ⋊ C2×D1491
SylowC3 ⋊ C2×D2485

Subgroups

subgroupG/H
center, hypercenterC2D7455
commutator, cosocle, hypocenterC3×C5×C7×C71C22
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C71C2
LCSG ▷ C3×C5×C7×C71
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 88
transitive degreeμt(G) = 14910

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

Conjugacy classes & character table

7458 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD29820
maximal normal subgroup ofD29820
maximal quotient ofDic14910, D29820

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 176);