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C11×C3⋊#157 #11924707

order1188
isoclinismisoclinic class of C3⋊#157
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊#157
unambiguous semidirect productC3⋊(C11×#157)

Splittings

Fitting, socle, HallC33×C11 ⋊ C4
derived, SylowC33 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#157
commutator, hypocenterC33C4×C11
FrattiniC1G
Fitting, socleC33×C11C4
prime radicalC3×C11×C3⋊D3C2
cosocleC3×C3⋊D3C2×C11
LCSG ▷ C33
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(15,16)(17,18,20,19);(12,13,14)(15,17,20)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 77);