Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | M64×D67 |
| Fitting | M64×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D67 |
| commutator, socle | C2×C67 | C22×C16 |
| Fitting | M64×C67 | C2 |
| hypercenter | M64 | D67 |
| hypocenter | C67 | C2×M64 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C16 ◁ M64 | |
112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 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 | #1398×D67, #30776017, #1400×D67, … |
| maximal normal subgroup of | #1398×D67, #30776017, #1400×D67, … |
| maximal quotient of | #1397×D67, M64×Dic67, #30776007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6800);