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(D33⋊C4)⋊C5 #13050313

order1320
isoclinismisoclinic class of D3×AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(D33⋊C4)⋊C5
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊C4

Splittings

derived, HallC3×C11 ⋊ C2×C4×C5
HallD33⋊C4 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C4
HallC11⋊C5 ⋊ C4×D3
SylowC11 ⋊ C4×C5×D3
SylowC3 ⋊ C4×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D3×AGL(1,𝔽11)
commutator, hypocenterC3×C11C2×C4×C5
Fitting, socle, cosocleC2×C3×C11C22×C5
prime radicalC2×C3⋊AGL(1,𝔽11)C2
LCSG ▷ C3×C11
UCSC1 ◁ C2

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Polycyclic presentation:

2^2,5,2,3,11|a^2=d,b^2=d,f^a=f^10,e^b=e^2,f^c=f^9

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D3×AGL(1,𝔽11), C2×(D33⋊C4)⋊C5, #72216761, …
maximal normal subgroup ofC4×D3×AGL(1,𝔽11), C2×(D33⋊C4)⋊C5, #72216761, …
maximal quotient ofC2×(D33⋊C4)⋊C5, #72216797, #72216801, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 17);