Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#11761611 |
| Fitting | C8×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ Q8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | C8×Q8×C67 | C2 |
| hypercenter | C8×Q8 | D67 |
| hypocenter | C67 | Q8×M16 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ C8×Q8 | |
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30826749, #30826755, #30826760, … |
| maximal normal subgroup of | #30826749, #30826755, #30826760, … |
| maximal quotient of | C4⋊C4×#11761611, #30854478, Q8×#14523953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13460);