Finite Group Databasebeta

← Prev (#49141635) Next (#49141637) →

C5×C3⋊D3×D203 #49141636

order36540
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C3⋊D3×D203

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C22
derived, HallC32×C7×C29 ⋊ C22×C5
HallC32×C5×C29 ⋊ C2×D7
HallC5×C7×C29 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D29
HallC32×C29 ⋊ C2×C5×D7
HallC7×C29 ⋊ C2×C5×C3⋊D3
HallC5×C29 ⋊ D7×C3⋊D3
HallC32×C7 ⋊ C2×C5×D29
HallC32×C5 ⋊ C2×D203
HallC5×C7 ⋊ C3⋊D3×D29
SylowC29 ⋊ C5×D7×C3⋊D3
SylowC32 ⋊ C2×C5×D203
SylowC7 ⋊ C5×C3⋊D3×D29

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D3×D203
commutator, cosocle, hypocenterC32×C7×C29C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C7×C29
UCSC1 ◁ C5

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 47
transitive degreeμt(G) = 9135

A minimal faithful permutation representation — 3 generators on 47 points:

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

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, 478);