Finite Group Databasebeta

← Prev (#13051568) Next (#13051570) →

#89437⋊C3 #13051569

order1344
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

unambiguous semidirect product#89437⋊C3

Splittings

FittingC7×#95 ⋊ C2×C3
Hall#89437 ⋊ C3
HallΓL(1,𝔽8) ⋊ #386
SylowC7 ⋊ C3×#386

Subgroups

subgroupG/H
center, FrattiniC23C22×AGL(1,𝔽7)
commutatorC22×C7C22×C3×C4
FittingC7×#95C2×C3
socle, cosocleC23×C7C23×C3
prime radicalC22×C4⋊AGL(1,𝔽7)C2
hypercenter#95AGL(1,𝔽7)
hypocenterC7C3×#386
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ #95

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Polycyclic presentation:

2^3,3,2^3,7|b^2=g,c^2=e,b^a=bg,h^a=h^6,c^b=cf,h^d=h^2

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72218436, C4×#6445⋊C3, #72218607, …
maximal normal subgroup ofC4×#6445⋊C3, #72218607, AGL(1,𝔽7)×#386, …
maximal quotient of#72218436, #72229510, #72276621, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 858);