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C2×C11×C19⋊C3 #11929418

order1254
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C19⋊C3
unambiguous semidirect product(C2×C19)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C19)⋊C3

Splittings

Fitting, socle, HallC2×C11×C19 ⋊ C3
derived, SylowC19 ⋊ C2×C3×C11
HallC11×C19 ⋊ C2×C3
HallC2×C19 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11C19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C19C3
LCSG ▷ C19
UCSC1 ◁ C2×C11

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 418

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×(C19⋊C3)⋊C4, Dic11×C19⋊C3, C11⋊((C19⋊C3)⋊C4), …
maximal normal subgroup ofC11×(C19⋊C3)⋊C4, Dic11×C19⋊C3, C11⋊((C19⋊C3)⋊C4), …
maximal quotient ofC4×C11×C19⋊C3, C22×C11×C19⋊C3, C2×C11×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1254, 4);