Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#14524051 |
| Fitting | C22×M16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C24×C4 |
| Frattini | C4 | C24×D67 |
| Fitting | C22×M16×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C22×M16 | D67 |
| hypocenter | C67 | C22×#131 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761244, #30761248, #30761262, … |
| maximal normal subgroup of | #30761244, #30761248, #30761262, … |
| maximal quotient of | C22×#16863353, C22×#16863354, C2×C4×#14524051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19216);