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C5×D9×D203 #49141271

order36540
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D9×D203
unambiguous semidirect product(C7×D9)⋊(C5×D29)
unambiguous semidirect product(D9×C29)⋊(C5×D7)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C22
derived, HallC7×C9×C29 ⋊ C22×C5
HallC5×C9×C29 ⋊ C2×D7
HallC5×C7×C29 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D29
HallC9×C29 ⋊ C2×C5×D7
HallC7×C29 ⋊ C2×C5×D9
HallC5×C29 ⋊ D7×D9
HallC7×C9 ⋊ C2×C5×D29
HallC5×C9 ⋊ C2×D203
HallC5×C7 ⋊ D9×D29
SylowC29 ⋊ C5×D7×D9
SylowC9 ⋊ C2×C5×D203
SylowC7 ⋊ C5×D9×D29

Subgroups

subgroupG/H
center, hypercenterC5D9×D203
commutator, cosocle, hypocenterC7×C9×C29C22×C5
FrattiniC3C5×D3×D203
FittingC5×C7×C9×C29C22
socleC3×C5×C7×C29C2×D3
LCSG ▷ C7×C9×C29
UCSC1 ◁ C5

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 9135

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,18,16,15,20,17,19,14,21)(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)(49,50);(6,7,9,11,12,10,8)(14,16)(15,19)(17,20)(18,21)(22,23,25,27,29,31,33,35,37,39,41,43,45,47,49,50,48,46,44,42,40,38,36,34,32,30,28,26,24)

Conjugacy classes & character table

3090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 113);