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C2×D6083 #37566659

order24332
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12166
direct productC2×D6083
unambiguous semidirect product(C2×C7)⋊D869
unambiguous semidirect product(C2×C11)⋊D553
unambiguous semidirect product(C2×C79)⋊D77

Splittings

Fitting, socleC2×C7×C11×C79 ⋊ C2
derived, HallC7×C11×C79 ⋊ C22
HallC11×C79 ⋊ C2×D7
HallC7×C79 ⋊ C2×D11
SylowC79 ⋊ C2×D77
HallC7×C11 ⋊ C2×D79
SylowC11 ⋊ C2×D553
SylowC7 ⋊ C2×D869

Subgroups

subgroupG/H
center, hypercenterC2D6083
commutator, cosocle, hypocenterC7×C11×C79C22
FrattiniC1G
Fitting, socleC2×C7×C11×C79C2
LCSG ▷ C7×C11×C79
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 99
transitive degreeμt(G) = 12166

A minimal faithful permutation representation — 2 generators on 99 points:

(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(4,9)(5,8)(6,7)(11,20)(12,19)(13,18)(14,17)(15,16)(22,99)(23,98)(24,97)(25,96)(26,95)(27,94)(28,93)(29,92)(30,91)(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Conjugacy classes & character table

6086 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD24332
maximal normal subgroup ofD24332
maximal quotient ofDic12166, D24332

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24332, 23);