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C2×D7755 #44526697

order31020
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15510
direct productC2×D7755
unambiguous semidirect product(C2×C3)⋊D2585
unambiguous semidirect product(C2×C5)⋊D1551
unambiguous semidirect product(C2×C11)⋊D705
unambiguous semidirect product(C2×C47)⋊D165

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC3×C5×C11×C47 ⋊ C22
HallC5×C11×C47 ⋊ C2×D3
HallC3×C11×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C2×D11
HallC11×C47 ⋊ C2×D15
HallC5×C47 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D47
HallC3×C47 ⋊ C2×D55
HallC5×C11 ⋊ C2×D141
SylowC47 ⋊ C2×D165
HallC3×C11 ⋊ C2×D235
HallC3×C5 ⋊ C2×D517
SylowC11 ⋊ C2×D705
SylowC5 ⋊ C2×D1551
SylowC3 ⋊ C2×D2585

Subgroups

subgroupG/H
center, hypercenterC2D7755
commutator, cosocle, hypocenterC3×C5×C11×C47C22
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C3×C5×C11×C47
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 68
transitive degreeμt(G) = 15510

A minimal faithful permutation representation — 2 generators on 68 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);(4,5)(7,10)(8,9)(12,21)(13,20)(14,19)(15,18)(16,17)(23,68)(24,67)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

7758 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31020
maximal normal subgroup ofD31020
maximal quotient ofDic15510, D31020

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 100);