Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #67369 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | C32×C7 ⋊ C3×C8 |
| Hall | C7⋊H(3,𝔽3) ⋊ C8 |
| Sylow | C7 ⋊ (C3⋊(C3⋊C8))⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #67369 |
| commutator, hypocenter | C32×C7 | C3×C8 |
| Frattini | C3×C4 | C3⋊AGL(1,𝔽7) |
| Fitting, cosocle | C32×C4×C7 | C2×C3 |
| socle | C2×C3×C7 | C3×Dic3 |
| prime radical | C2×C7⋊H(3,𝔽3) | C4 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C4 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2,3,2^2,3^2,7|a^2=c,c^2=d,e^a=e^2,f^a=f^2,g^a=g^6,e^b=ef,g^b=g^276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 57);