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C5×D23×D63 #44394387

order28980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D23×D63
unambiguous semidirect product(C7×D23)⋊(C5×D9)
unambiguous semidirect product(C9×D23)⋊(C5×D7)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C22
derived, HallC7×C9×C23 ⋊ C22×C5
HallC5×C9×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D23
HallC9×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C2×C5×D9
HallC5×C23 ⋊ C2×D63
HallC7×C9 ⋊ C2×C5×D23
HallC5×C9 ⋊ D7×D23
HallC5×C7 ⋊ D9×D23
SylowC23 ⋊ C2×C5×D63
SylowC9 ⋊ C5×D7×D23
SylowC7 ⋊ C5×D9×D23

Subgroups

subgroupG/H
center, hypercenterC5D23×D63
commutator, cosocle, hypocenterC7×C9×C23C22×C5
FrattiniC3C5×D21×D23
FittingC5×C7×C9×C23C22
socleC3×C5×C7×C23C2×D3
LCSG ▷ C7×C9×C23
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) = 44
transitive degreeμt(G) = 7245

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 56);