Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #124×Dic67 |
| Sylow | C67 ⋊ C4×#124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | C2×#124×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C2×#124 | D67 |
| hypocenter | C67 | C4×#124 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #329×Dic67, #30746755, #30746763, … |
| maximal normal subgroup of | #329×Dic67, #30746755, #30746763, … |
| maximal quotient of | #388×Dic67, #390×Dic67, #391×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7055);