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D3×#11762245⋊C5 #44570502

order32490
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD3×#11762245⋊C5
unambiguous semidirect productC3⋊(C2×#11762245⋊C5)
unambiguous semidirect product(D3×#11762245)⋊C5
unambiguous semidirect product(D3×C192⋊C5)⋊C3

Splittings

Fitting, socle, derivedC3×C192 ⋊ C2×C3×C5
HallC3×#11762245⋊C5 ⋊ C2
HallD3×#11762245 ⋊ C5
HallC3×#11762245 ⋊ C2×C5
HallC192⋊C5 ⋊ C3×D3
SylowC192 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C192C2×C3×C5
LCSG ▷ C3×C192
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 98
transitive degreeμt(G) = 285

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

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

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 86);