Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16863457 |
| Sylow | C67 ⋊ C2×#433 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C22×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×#117×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×#117 | D67 |
| hypocenter | C67 | C2×#433 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
412 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746369, #30748698, C4×#16863457, … |
| maximal normal subgroup of | #30746369, #30748698, C4×#16863457, … |
| maximal quotient of | C2×#22559961, C2×#22559975, C2×#22560066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13136);