Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C2×#97×D67 |
| Fitting | C2×#97×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C22×C42 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×#97×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×#97 | D67 |
| hypocenter | C67 | C22×#97 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 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 | #1275×D67, #30745251, #1281×D67, … |
| maximal normal subgroup of | #1275×D67, #30745251, #1281×D67, … |
| maximal quotient of | C2×#322×D67, #1451×D67, C2×#22558495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12912);