Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16863955 |
| Fitting | C23×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#534 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D67 |
| commutator | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C23×D4×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C23×D4 | D67 |
| hypocenter | C67 | C2×#534 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
1984 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30762351, #30762352, #30762355, … |
| maximal normal subgroup of | #30762351, #30762352, #30762355, … |
| maximal quotient of | C2×#22562784, C2×#22562787, C2×#22562821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17810);