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C5×D33⋊D39 #38788230

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

Aliases

direct productC5×D33⋊D39

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derived, HallC32×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ D32
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C5×D32
HallC32×C13 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ (C3⋊D3)⋊D11
HallC5×C11 ⋊ D3×D39
HallC32×C5 ⋊ D11×D13
SylowC13 ⋊ C5×(C3⋊D3)⋊D11
SylowC11 ⋊ C5×D3×D39
SylowC32 ⋊ C5×D11×D13

Subgroups

subgroupG/H
center, hypercenterC5D33⋊D39
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 4290

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5)(6,7,9,11,13,15,17,18,16,14,12,10,8)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31,32)(33,34);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20,22,24,26,28,29,27,25,23,21)(31,32)(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(25740, 461);