Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×C67⋊C8 |
| Sylow | C67 ⋊ C2×C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C23×C8 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×C4×D4×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×C4×D4 | D67 |
| hypocenter | C67 | C2×C8×D4 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
616 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×C67⋊C8, #30746375, #30746379, … |
| maximal normal subgroup of | #99×C67⋊C8, #30746375, #30746379, … |
| maximal quotient of | C2×D8×C67⋊C8, C2×SD16×C67⋊C8, C2×Q16×C67⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13183);