Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#41×D67 |
| Fitting | C22×#41×C67 ⋊ C2 |
| Sylow | C67 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C26 |
| Frattini | C2 | C25×D67 |
| Fitting | C22×#41×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C22×#41 | D67 |
| hypocenter | C67 | C23×#41 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
6520 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1780×D67, #30854942, #30854946, … |
| maximal normal subgroup of | #1780×D67, #30854942, #30854946, … |
| maximal quotient of | C22×#117×D67, C22×C4×D4×D67, C22×C4×Q8×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19306);