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C5×D19×D63 #37561002

order23940
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D19×D63
unambiguous semidirect product(C7×D19)⋊(C5×D9)
unambiguous semidirect product(C9×D19)⋊(C5×D7)

Splittings

Fitting, HallC5×C7×C9×C19 ⋊ C22
derived, HallC7×C9×C19 ⋊ C22×C5
HallC5×C9×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D19
HallC9×C19 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C5×D9
HallC5×C19 ⋊ C2×D63
HallC7×C9 ⋊ C2×C5×D19
HallC5×C9 ⋊ D7×D19
HallC5×C7 ⋊ D9×D19
SylowC19 ⋊ C2×C5×D63
SylowC9 ⋊ C5×D7×D19
SylowC7 ⋊ C5×D9×D19

Subgroups

subgroupG/H
center, hypercenterC5D19×D63
commutator, cosocle, hypocenterC7×C9×C19C22×C5
FrattiniC3C5×D19×D21
FittingC5×C7×C9×C19C22
socleC3×C5×C7×C19C2×D3
LCSG ▷ C7×C9×C19
UCSC1 ◁ C5

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 40
transitive degreeμt(G) = 5985

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

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

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 134);