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C2×C5×D1071 #36339286

order21420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1071
unambiguous semidirect product(C2×C7)⋊(C5×D153)
unambiguous semidirect product(C2×C9)⋊(C5×D119)
unambiguous semidirect product(C2×C17)⋊(C5×D63)

Splittings

FittingC2×C5×C7×C9×C17 ⋊ C2
derived, HallC7×C9×C17 ⋊ C22×C5
HallC5×C7×C9×C17 ⋊ C22
HallC5×C9×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D17
HallC9×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×C5×D9
HallC5×C17 ⋊ C2×D63
HallC7×C9 ⋊ C2×C5×D17
HallC5×C9 ⋊ C2×D119
HallC5×C7 ⋊ C2×D153
SylowC17 ⋊ C2×C5×D63
SylowC9 ⋊ C2×C5×D119
SylowC7 ⋊ C2×C5×D153

Subgroups

subgroupG/H
center, hypercenterC2×C5D1071
commutator, cosocle, hypocenterC7×C9×C17C22×C5
FrattiniC3C2×C5×D357
FittingC2×C5×C7×C9×C17C2
socleC2×C3×C5×C7×C17D3
LCSG ▷ C7×C9×C17
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 10710

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

5370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 118);