Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16863527 |
| Sylow | C67 ⋊ C2×#446 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C22×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×C4×Q8×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×C4×Q8 | D67 |
| hypocenter | C67 | C2×#446 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
400 conjugacy classes of subgroups.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746419, #30746421, #30746659, … |
| maximal normal subgroup of | #30746419, #30746421, #30746659, … |
| maximal quotient of | C2×#22560084, C2×#22560078, C4×#16863527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13438);