Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×C67⋊C8 |
| Sylow | C67 ⋊ C8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D67 |
| commutator | C2×C67 | C2×C4×C8 |
| Fitting | C4×M16×C67 | C2 |
| socle | C22×C67 | C2×C42 |
| hypercenter | C4×M16 | D67 |
| hypocenter | C67 | C8×M16 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C42 ◁ C4×M16 | |
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 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 | #30746388, #100×C67⋊C8, #30746393, … |
| maximal normal subgroup of | #30746388, #100×C67⋊C8, #30746393, … |
| maximal quotient of | #97×C67⋊C8, #30745212, #30746256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2788);