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C11×D91⋊(C3⋊D3) #49114987

order36036
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC11×D91⋊(C3⋊D3)
unambiguous semidirect productD91⋊(C11×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derived, HallC32×C7×C13 ⋊ C22×C11
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ D7×C3⋊D3
HallC32×C13 ⋊ C2×C11×D7
HallC32×C11 ⋊ D7×D13
HallC7×C13 ⋊ C2×C11×C3⋊D3
HallC7×C11 ⋊ C3⋊D3×D13
HallC32×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C11×D7×C3⋊D3
SylowC32 ⋊ C11×D7×D13
SylowC7 ⋊ C11×C3⋊D3×D13

Subgroups

subgroupG/H
center, hypercenterC11D91⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

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) = 37
transitive degreeμt(G) = 9009

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

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

Conjugacy classes & character table

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 655);