Finite Group Databasebeta

← Prev (#40997667) Next (#40997669) →

C2×C3⋊(C3⋊(D67⋊C11)) #40997668

order26532
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊(C3⋊(D67⋊C11))
unambiguous semidirect product(C2×C3)⋊(C3⋊(D67⋊C11))
unambiguous semidirect product(C2×C67⋊C11)⋊(C3⋊D3)
unambiguous semidirect product(C2×C3⋊D201)⋊C11

Splittings

Fitting, socleC2×C32×C67 ⋊ C2×C11
derived, HallC32×C67 ⋊ C22×C11
HallC32×C67⋊C11 ⋊ C22
HallC2×C3⋊D201 ⋊ C11
HallC67⋊C11 ⋊ C2×C3⋊D3
SylowC67 ⋊ C2×C11×C3⋊D3
SylowC32 ⋊ C2×D67⋊C11

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(D67⋊C11))
commutator, cosocle, hypocenterC32×C67C22×C11
FrattiniC1G
Fitting, socleC2×C32×C67C2×C11
LCSG ▷ C32×C67
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 75
transitive degreeμt(G) = 1206

A minimal faithful permutation representation — 3 generators on 75 points:

(2,6,7,17,22,43,18,57,16,40,53,3,4,10,12,32,41,34,35,21,31,61)(5,14,15,48,33,65,66,30,24,25,62,8,9,27,29,55,49,54,51,13,44,45)(11,37,38,23,39,47,64,46,67,28,58,19,20,59,42,26,60,63,56,52,36,50)(69,70)(72,73);(1,2,5,6,11,21,14,28,34,7,13,26,37,29,22,31,54,65,15,30,52,58,53,45,35,41,42,17,33,56,44,59,63,60,47,64,38,25,46,55,12,23,43,57,62,61,50,67,51,27,49,66,40,32,48,20,39,24,10,18,36,9,16,19,4,8,3)(71,72,73)(74,75);(68,69,70)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26532, 99);