Finite Group Databasebeta

← Prev (#13050315) Next (#13050317) →

#63142⋊C5 #13050316

order1320
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#63142⋊C5

Splittings

Hall#63142 ⋊ C5
HallC3×C11⋊C5 ⋊ D4
HallC11⋊C5 ⋊ D12
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C5×D12
SylowC3 ⋊ C22⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D3×AGL(1,𝔽11)
commutator, Fitting, socle, cosocleC2×C3×C11C22×C5
hypocenterC3×C11C5×D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 132

Polycyclic presentation:

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

Conjugacy classes & character table

51 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD12×AGL(1,𝔽11), D3×C22⋊AGL(1,𝔽11), #72216761, …
maximal normal subgroup ofD12×AGL(1,𝔽11), D3×C22⋊AGL(1,𝔽11), #72216761, …
maximal quotient ofC2×#63142⋊C5, #72216803, #72216807, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 20);