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C2×C5×D1813 #49136387

order36260
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1813
unambiguous semidirect product(C2×C37)⋊(C5×D49)
unambiguous semidirect product(C2×C49)⋊(C5×D37)

Splittings

FittingC2×C5×C37×C49 ⋊ C2
derived, HallC37×C49 ⋊ C22×C5
HallC5×C37×C49 ⋊ C22
HallC5×C49 ⋊ C2×D37
HallC5×C37 ⋊ C2×D49
SylowC49 ⋊ C2×C5×D37
SylowC37 ⋊ C2×C5×D49

Subgroups

subgroupG/H
center, hypercenterC2×C5D1813
commutator, cosocle, hypocenterC37×C49C22×C5
FrattiniC7C2×C5×D259
FittingC2×C5×C37×C49C2
socleC2×C5×C7×C37D7
LCSG ▷ C37×C49
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 18130

A minimal faithful permutation representation — 2 generators on 93 points:

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

Conjugacy classes & character table

9080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36260, 33);