Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #382×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2820 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | #382×C67 | C2 |
| hypercenter | #382 | D67 |
| hypocenter | C67 | #2820 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #382 | |
464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=ef,b^2=e,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,h^b=h^66,d^c=de,h^c=h^66950 conjugacy classes — view the full character table.
| maximal subgroup of | #30757115, #30757119, #30757134, … |
| maximal normal subgroup of | #30757115, #30757119, #30757134, … |
| maximal quotient of | #30786503, #30786525, #30786545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12562);