Finite Group Databasebeta

← Prev (#13050332) Next (#13050334) →

#63159⋊C5 #13050333

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

Aliases

unambiguous semidirect product#63159⋊C5

Splittings

FittingC22×C3×C11 ⋊ C2×C5
Hall#63159 ⋊ C5
HallC3×C11⋊C5 ⋊ D4
HallC11⋊C5 ⋊ #67
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C5×#67
SylowC3 ⋊ C22⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, FrattiniC2C2×C3⋊AGL(1,𝔽11)
commutator, socle, cosocleC2×C3×C11C22×C5
FittingC22×C3×C11C2×C5
hypercenterC22C3⋊AGL(1,𝔽11)
hypocenterC3×C11C5×D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ C22

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|b^a=bd,e^a=e^2,f^a=f^10,f^c=f^5

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×C3⋊AGL(1,𝔽11), D3×C22⋊AGL(1,𝔽11), #67×AGL(1,𝔽11), …
maximal normal subgroup ofD4×C3⋊AGL(1,𝔽11), D3×C22⋊AGL(1,𝔽11), #67×AGL(1,𝔽11), …
maximal quotient ofC2×#63159⋊C5, #72216823, #72216828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 37);