Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#16863307 |
| Fitting | C23×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#393 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C23×C67 | C24 |
| Frattini | C23 | C23×D67 |
| Fitting | C23×Q8×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C23×Q8 | D67 |
| hypocenter | C67 | C2×#393 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750817, #30750832, #30756038, … |
| maximal normal subgroup of | #30750817, #30750832, #30756038, … |
| maximal quotient of | C2×#22558451, C2×#22558468, C2×#22558480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7709);