Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×Q8×D67 |
| Fitting | C23×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C2×C67 | C26 |
| Frattini | C2 | C25×D67 |
| Fitting | C23×Q8×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C23×Q8 | D67 |
| hypocenter | C67 | C24×Q8 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
6264 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1446×D67, #30778215, #30778218, … |
| maximal normal subgroup of | #1446×D67, #30778215, #30778218, … |
| maximal quotient of | C23×C4⋊C4×D67, C22×C4×Q8×D67, C23×#14524008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19304);