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(C33⋊C13)⋊C3 #11760457

order1053
isoclinismisoclinic class of (C33⋊C13)⋊C3
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C33⋊C13)⋊C3

Splittings

Fitting, socleC33 ⋊ C13⋊C3
derivedC33⋊C13 ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC33⋊C13C3
Fitting, socleC33C13⋊C3
LCSG ▷ C33⋊C13
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 27

Polycyclic presentation:

3,13,3^3|b^a=b^3,c^a=cde,d^a=de^2,c^b=cd,d^b=de,e^b=c^2e^2

Conjugacy classes & character table

13 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C33⋊C13)⋊C3, PΣL(2,𝔽27), AΓL(1,𝔽27), …
maximal normal subgroup ofC3×(C33⋊C13)⋊C3, AΓL(1,𝔽27), C2×(C33⋊C13)⋊C3
maximal quotient of(C33⋊C13)⋊C9, C3×(C33⋊C13)⋊C3, C2×(C33⋊C13)⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1053, 51);