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C3×C5⋊((C19⋊C3)⋊D19) #44570587

order32490
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊((C19⋊C3)⋊D19)
unambiguous semidirect productC5⋊(C3×(C19⋊C3)⋊D19)
unambiguous semidirect product(C19⋊C3)⋊(C3×D95)

Splittings

Fitting, socleC3×C5×C192 ⋊ C2×C3
derived, HallC5×C192 ⋊ C2×C32
HallC3×C5×C19×C19⋊C3 ⋊ C2
HallC5⋊(C19⋊D19) ⋊ C32
HallC3×C19×C19⋊C3 ⋊ D5
SylowC192 ⋊ C32×D5
SylowC5 ⋊ C3×(C19⋊C3)⋊D19

Subgroups

subgroupG/H
center, hypercenterC3C5⋊((C19⋊C3)⋊D19)
commutator, cosocle, hypocenterC5×C192C2×C32
FrattiniC1G
Fitting, socleC3×C5×C192C2×C3
LCSG ▷ C5×C192
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 855

A minimal faithful permutation representation — 2 generators on 46 points:

(5,6)(7,8)(10,14,15,11,12,16)(13,22,19,17,18,24)(20,25,27,26,23,21)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46);(1,2,3)(4,5,7,8,6)(9,10,13,19,25,22,26,12,16,21,27,15,14,20,18,23,24,17,11)(28,29,31,33,35,37,39,41,43,45,46,44,42,40,38,36,34,32,30)

Conjugacy classes & character table

1296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 171);