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C17×#711 #13062833

order1360
automorphism?
homologyAbelianization (H1) = C23×C17 · Schur multiplier (H2) = C22

Aliases

direct productC17×#711

Splittings

FittingC5×D4×C17 ⋊ C2
HallC5×C17 ⋊ #41
SylowC5 ⋊ #41×C17

Subgroups

subgroupG/H
centerC2×C17C22×D5
commutator, cosocleC2×C5C23×C17
FrattiniC2C22×D5×C17
FittingC5×D4×C17C2
socleC2×C5×C17C23
hypercenterD4×C17D5
hypocenterC5#41×C17
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C17 ◁ D4×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 680

A minimal faithful permutation representation — 3 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,22,20)(24,28)(25,29);(23,25,26,29)(24,27,28,30);(19,20)(21,22)(23,24)(25,27)(26,28)(29,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 201);