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C2×C17×C3⋊(C13⋊D13) #46828390

order34476
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C13

Aliases

direct productC2×C17×C3⋊(C13⋊D13)
unambiguous semidirect product(C2×C3)⋊(C17×C13⋊D13)
unambiguous semidirect product(C2×C13)⋊(C17×D39)

Splittings

Fitting, socleC2×C3×C132×C17 ⋊ C2
derived, HallC3×C132 ⋊ C22×C17
HallC3×C132×C17 ⋊ C22
HallC132×C17 ⋊ C2×D3
SylowC132 ⋊ C2×D3×C17
HallC3×C17 ⋊ C2×C13⋊D13
SylowC3 ⋊ C2×C17×C13⋊D13

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(C13⋊D13)
commutator, cosocle, hypocenterC3×C132C22×C17
FrattiniC1G
Fitting, socleC2×C3×C132×C17C2
LCSG ▷ C3×C132
UCSC1 ◁ C2×C17

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 17238

A minimal faithful permutation representation — 3 generators on 48 points:

(4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(1,2)(3,4,5)(19,20,22,24,26,28,30,31,29,27,25,23,21);(6,7,9,11,13,15,17,18,16,14,12,10,8)

Conjugacy classes & character table

8670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 271);