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C22×C32×C11⋊C5 #14520447

order1980
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C32×C11⋊C5
unambiguous semidirect product(C22×C32×C11)⋊C5

Splittings

Fitting, socle, HallC22×C32×C11 ⋊ C5
derived, SylowC11 ⋊ C22×C32×C5
HallC32×C11 ⋊ C22×C5
HallC22×C11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC22×C32C11⋊C5
commutator, cosocle, hypocenterC11C22×C32×C5
FrattiniC1G
Fitting, socleC22×C32×C11C5
LCSG ▷ C11
UCSC1 ◁ C22×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 396

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2)(5,6,7)(12,13,15,18,17)(14,16,20,21,19);(3,4)(8,9,10)(11,12,14,17,13,15,19,21,16,18,20)

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽7)×C11⋊C5, C22×C3×ΓL(1,𝔽8)×C11⋊C5, C2×C32×D7×C11⋊C5, …
maximal normal subgroup ofC22×C32×C7×C11⋊C5, C22×C32×C11×C11⋊C5, C22×C32×C13×C11⋊C5, …
maximal quotient ofC2×C3×AGL(1,𝔽7)×C11⋊C5, C22×C3×ΓL(1,𝔽8)×C11⋊C5, C2×C32×D7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 72);