Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×#11761628 |
| Fitting | C2×C4×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C2×C4×D4×C67 | C2 |
| hypercenter | C2×C4×D4 | D67 |
| hypocenter | C67 | D4×#41 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
1648 conjugacy classes of subgroups.
1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747851, #30747855, #30822687, … |
| maximal normal subgroup of | #30747851, #30747855, #30822687, … |
| maximal quotient of | C22⋊C4×#11761628, C4⋊C4×#11761628, D4×#14524000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17998);