Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×Q8×D67 |
| Fitting | D4×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | D4×Q8×C67 | C2 |
| hypercenter | D4×Q8 | D67 |
| hypocenter | C67 | C2×D4×Q8 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1568 conjugacy classes of subgroups.
875 conjugacy classes — view the full character table.
| maximal subgroup of | #1627×D67, #1637×D67, #1651×D67, … |
| maximal normal subgroup of | #1627×D67, #1637×D67, #1651×D67, … |
| maximal quotient of | Q8×C22⋊C4×D67, D4×C4⋊C4×D67, Q8×C4⋊C4×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17980);