Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#14524089 |
| Fitting | C22×#41×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D67 |
| commutator | C2×C67 | C26 |
| Frattini | C2 | C25×D67 |
| Fitting | C22×#41×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C22×#41 | D67 |
| hypocenter | C67 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30854966, #30854970, #30854998, … |
| maximal normal subgroup of | #30854966, #30854970, #30854998, … |
| maximal quotient of | C22×#16863868, C22×#16863870, C22×#16863876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19312);