Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C23×D4×D67 |
| Fitting | C23×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C2×C67 | C26 |
| Frattini | C2 | C25×D67 |
| Fitting | C23×D4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C23×D4 | D67 |
| hypocenter | C67 | C24×D4 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
10552 conjugacy classes of subgroups; only the 3557 normal subgroups are shown.
This group has 10552 conjugacy classes of subgroups — too many to draw. Only its 3557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1438×D67, #30777696, #30777699, … |
| maximal normal subgroup of | #1438×D67, #30777696, #30777699, … |
| maximal quotient of | C23×C22⋊C4×D67, C23×C4⋊C4×D67, C22×C4×D4×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19301);