Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | #392×D67 |
| Fitting | #392×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | #392×C67 | C2 |
| hypercenter | #392 | D67 |
| hypocenter | C67 | C2×#392 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #392 | |
1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #1343×D67, #30766485, #1595×D67, … |
| maximal normal subgroup of | #1343×D67, #30766485, #1595×D67, … |
| maximal quotient of | #1438×D67, #1439×D67, #1444×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7704);