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C5×C11×C22⋊C9 #14520405

order1980
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×C22⋊C9
unambiguous semidirect productC22⋊(C5×C9×C11)
unambiguous semidirect product(C22×C5)⋊(C9×C11)
unambiguous semidirect product(C22×C5×C11)⋊C9

Splittings

derived, SylowC22 ⋊ C5×C9×C11
HallC22×C5×C11 ⋊ C9
HallC22×C11 ⋊ C5×C9
HallC22×C5 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11A4
commutator, hypocenterC22C5×C9×C11
FrattiniC3C5×C11×A4
Fitting, socle, prime radicalC22×C3×C5×C11C3
cosocleC22×C3C3×C5×C11
LCSG ▷ C22
UCSC1 ◁ C3×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 990

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C7×C11×C22⋊C9, C5×C11×C22⋊(C7⋊C9), C5×C22⋊C9×C121, …
maximal normal subgroup ofC5×C7×C11×C22⋊C9, C5×C22⋊C9×C121, C5×C112×C22⋊C9, …
maximal quotient ofC5×C7×C11×C22⋊C9, C5×C11×C22⋊(C7⋊C9), C5×C22⋊C9×C121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 30);