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C2×C5⋊((C13⋊D13)⋊C7) #37556844

order23660
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C13

Aliases

direct productC2×C5⋊((C13⋊D13)⋊C7)
unambiguous semidirect product(C2×C5)⋊((C13⋊D13)⋊C7)
unambiguous semidirect product(C2×C5⋊(C13⋊D13))⋊C7

Splittings

Fitting, socleC2×C5×C132 ⋊ C2×C7
derived, HallC5×C132 ⋊ C22×C7
HallC5×C132⋊C7 ⋊ C22
HallC2×C5⋊(C13⋊D13) ⋊ C7
HallC132⋊C7 ⋊ C2×D5
SylowC132 ⋊ C2×C7×D5
SylowC5 ⋊ C2×(C13⋊D13)⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C5⋊((C13⋊D13)⋊C7)
commutator, cosocle, hypocenterC5×C132C22×C7
FrattiniC1G
Fitting, socleC2×C5×C132C2×C7
LCSG ▷ C5×C132
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 98
transitive degreeμt(G) = 910

A minimal faithful permutation representation — 2 generators on 98 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23660, 74);