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C5×D143⋊(C3⋊D3) #38788265

order25740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×D143⋊(C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derived, HallC32×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ C2×C3⋊D3
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×C3⋊D3
HallC32×C13 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ C3⋊D3×D11
HallC5×C11 ⋊ C3⋊D3×D13
HallC32×C5 ⋊ D11×D13
SylowC13 ⋊ C5×C3⋊D3×D11
SylowC11 ⋊ C5×C3⋊D3×D13
SylowC32 ⋊ C5×D11×D13

Subgroups

subgroupG/H
center, hypercenterC5D143⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 35
transitive degreeμt(G) = 6435

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 496);