Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #398×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | #398×C67 | C2 |
| hypercenter | #398 | D67 |
| hypocenter | C67 | #2729 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #398 | |
480 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=ef,b^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^66,h^c=h^66,h^d=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #31063440, #31063443, #31063466, … |
| maximal normal subgroup of | #31063440, #31063443, #31063466, … |
| maximal quotient of | #30783619, #30783802, #30783841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 11491);