Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#14523968 |
| Sylow | C67 ⋊ C22×#103 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D268 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C23×C8×C67 | C2 |
| socle | C24×C67 | D4 |
| hypercenter | C23×C8 | D67 |
| hypocenter | C67 | C22×#103 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761399, #30761403, #30762097, … |
| maximal normal subgroup of | #30761399, #30761403, #30762097, … |
| maximal quotient of | C22×#16863128, C2×#22558639, C2×#22558613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13001);