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C2×D15477 #72297702

order61908
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD30954
direct productC2×D15477

Splittings

Fitting, socleC2×C3×C7×C11×C67 ⋊ C2
derived, HallC3×C7×C11×C67 ⋊ C22
HallC7×C11×C67 ⋊ C2×D3
HallC3×C11×C67 ⋊ C2×D7
HallC3×C7×C67 ⋊ C2×D11
HallC11×C67 ⋊ C2×D21
HallC7×C67 ⋊ C2×D33
HallC3×C7×C11 ⋊ C2×D67
HallC3×C67 ⋊ C2×D77
HallC7×C11 ⋊ C2×D201
SylowC67 ⋊ C2×D231
HallC3×C11 ⋊ C2×D469
HallC3×C7 ⋊ C2×D737
SylowC11 ⋊ C2×D1407
SylowC7 ⋊ C2×D2211
SylowC3 ⋊ C2×D5159

Subgroups

subgroupG/H
center, hypercenterC2D15477
commutator, cosocle, hypocenterC3×C7×C11×C67C22
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C67C2
LCSG ▷ C3×C7×C11×C67
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 90
transitive degreeμt(G) = 30954

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

Conjugacy classes & character table

15480 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), (4,5)(7,12)(8,11)(9,10)(14,23)(15,22)(16,21)(17,20)(18,19)(25,90)(26,89)(27,88)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58));