Finite Group Databasebeta

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C13×D11×C3⋊D21 #49114980

order36036
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC13×D11×C3⋊D21
unambiguous semidirect product(C3×D11)⋊(C13×D21)
unambiguous semidirect product(C7×D11)⋊(C13×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derived, HallC32×C7×C11 ⋊ C22×C13
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C13 ⋊ C2×D11
HallC11×C13 ⋊ C2×C3⋊D21
HallC32×C13 ⋊ D7×D11
HallC32×C11 ⋊ C2×C13×D7
HallC7×C13 ⋊ C3⋊D3×D11
HallC7×C11 ⋊ C2×C13×C3⋊D3
HallC32×C7 ⋊ C2×C13×D11
SylowC11 ⋊ C2×C13×C3⋊D21
SylowC32 ⋊ C13×D7×D11
SylowC7 ⋊ C13×C3⋊D3×D11

Subgroups

subgroupG/H
center, hypercenterC13D11×C3⋊D21
commutator, cosocle, hypocenterC32×C7×C11C22×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C13

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 37
transitive degreeμt(G) = 9009

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 648);