Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C67 ⋊ #2346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | #388×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #388 | D67 |
| hypocenter | C67 | #2346 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #388 | |
504 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=f,c^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^66,h^d=h^66974 conjugacy classes — view the full character table.
| maximal subgroup of | #2346×D67, C2×#22563091, #31015097, … |
| maximal normal subgroup of | #2346×D67, C2×#22563091, #31015097, … |
| maximal quotient of | #30777253, #30777280, #30777282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7392);