Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #543×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3459 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | #543×C67 | C2 |
| hypercenter | #543 | D67 |
| hypocenter | C67 | #3459 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #543 | |
1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|e^2=g,b^a=bf,c^a=cg,d^a=df,h^a=h^66,c^b=cf,h^c=h^66,h^e=h^66770 conjugacy classes — view the full character table.
| maximal subgroup of | #30827936, #30827942, #30827987, … |
| maximal normal subgroup of | #30827936, #30827942, #30827987, … |
| maximal quotient of | #31014505, #31014778, #31014793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17922);