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C2×D3255 #27189271

order13020
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD6510
direct productC2×D3255
unambiguous semidirect product(C2×C3)⋊D1085
unambiguous semidirect product(C2×C5)⋊D651
unambiguous semidirect product(C2×C7)⋊D465
unambiguous semidirect product(C2×C31)⋊D105

Splittings

Fitting, socleC2×C3×C5×C7×C31 ⋊ C2
derived, HallC3×C5×C7×C31 ⋊ C22
HallC5×C7×C31 ⋊ C2×D3
HallC3×C7×C31 ⋊ C2×D5
HallC3×C5×C31 ⋊ C2×D7
HallC7×C31 ⋊ C2×D15
HallC5×C31 ⋊ C2×D21
HallC3×C5×C7 ⋊ C2×D31
HallC3×C31 ⋊ C2×D35
HallC5×C7 ⋊ C2×D93
SylowC31 ⋊ C2×D105
HallC3×C7 ⋊ C2×D155
HallC3×C5 ⋊ C2×D217
SylowC7 ⋊ C2×D465
SylowC5 ⋊ C2×D651
SylowC3 ⋊ C2×D1085

Subgroups

subgroupG/H
center, hypercenterC2D3255
commutator, cosocle, hypocenterC3×C5×C7×C31C22
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C31C2
LCSG ▷ C3×C5×C7×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 6510

A minimal faithful permutation representation — 2 generators on 48 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);(4,5)(7,10)(8,9)(12,17)(13,16)(14,15)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Conjugacy classes & character table

3258 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13020, C2×D16275
maximal normal subgroup ofD13020
maximal quotient ofD13020, Dic6510, C2×D16275

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 238);