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C2×D8323 #45685652

order33292
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16646
direct productC2×D8323
unambiguous semidirect product(C2×C7)⋊D1189
unambiguous semidirect product(C2×C29)⋊D287
unambiguous semidirect product(C2×C41)⋊D203

Splittings

Fitting, socleC2×C7×C29×C41 ⋊ C2
derived, HallC7×C29×C41 ⋊ C22
HallC29×C41 ⋊ C2×D7
HallC7×C41 ⋊ C2×D29
HallC7×C29 ⋊ C2×D41
SylowC41 ⋊ C2×D203
SylowC29 ⋊ C2×D287
SylowC7 ⋊ C2×D1189

Subgroups

subgroupG/H
center, hypercenterC2D8323
commutator, cosocle, hypocenterC7×C29×C41C22
FrattiniC1G
Fitting, socleC2×C7×C29×C41C2
LCSG ▷ C7×C29×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 16646

A minimal faithful permutation representation — 2 generators on 79 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);(4,9)(5,8)(6,7)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

8326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33292, 50);