Finite Group Databasebeta

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C7×D13×C3⋊D33 #49114971

order36036
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC7×D13×C3⋊D33
unambiguous semidirect product(C3×D13)⋊(C7×D33)
unambiguous semidirect product(C11×D13)⋊(C7×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derived, HallC32×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C7×C3⋊D3
HallC32×C13 ⋊ C2×C7×D11
HallC32×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C3⋊D33
HallC7×C11 ⋊ C3⋊D3×D13
HallC32×C7 ⋊ D11×D13
SylowC13 ⋊ C2×C7×C3⋊D33
SylowC11 ⋊ C7×C3⋊D3×D13
SylowC32 ⋊ C7×D11×D13

Subgroups

subgroupG/H
center, hypercenterC7D13×C3⋊D33
commutator, cosocle, hypocenterC32×C11×C13C22×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C7

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

Conjugacy classes & character table

2856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 639);