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C2×C11×C3⋊(C3⋊(C7⋊D7)) #34085074

order19404
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3×C7

Aliases

direct productC2×C11×C3⋊(C3⋊(C7⋊D7))
unambiguous semidirect product(C2×C3)⋊(C11×C3⋊(C7⋊D7))
unambiguous semidirect product(C2×C7)⋊(C11×C3⋊D21)

Splittings

Fitting, socleC2×C32×C72×C11 ⋊ C2
derived, HallC32×C72 ⋊ C22×C11
HallC32×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×C3⋊D3
HallC32×C11 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C11×C3⋊D3
SylowC32 ⋊ C2×C11×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C3⋊(C7⋊D7))
commutator, cosocle, hypocenterC32×C72C22×C11
FrattiniC1G
Fitting, socleC2×C32×C72×C11C2
LCSG ▷ C32×C72
UCSC1 ◁ C2×C11

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 9702

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

4884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 565);