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C2×C5⋊(C11⋊(#4294⋊C2)) #49178366

order37620
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(C11⋊(#4294⋊C2))
unambiguous semidirect product(C2×C5)⋊(C11⋊(#4294⋊C2))
unambiguous semidirect product(C2×C11)⋊(C5⋊(#4294⋊C2))
unambiguous semidirect product(C2×#4294)⋊D55

Splittings

derived, HallC5×C11×C19 ⋊ C22×C9
HallC5×C11×#4294 ⋊ C22
HallC2×D1045 ⋊ C9
HallC11×#4294 ⋊ C2×D5
HallC5×#4294 ⋊ C2×D11
HallC11×C19 ⋊ C2×C9×D5
Hall#4294 ⋊ C2×D55
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C2×#4294⋊C2
SylowC19 ⋊ C2×C9×D55
SylowC11 ⋊ C2×C5⋊(#4294⋊C2)
SylowC5 ⋊ C2×C11⋊(#4294⋊C2)

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(C11⋊(D19⋊C3))
commutator, hypocenterC5×C11×C19C22×C9
FrattiniC3C2×C5⋊(C11⋊(D19⋊C3))
Fitting, socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×D1045C3
cosocleC3×C5×C11×C19C22×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 18810

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

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

Conjugacy classes & character table

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 75);