Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14523971 |
| Fitting | C43×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×#104 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | D268 |
| commutator | C4×C67 | C2×C42 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | C43×C67 | C2 |
| socle | C22×C67 | C2×C22⋊C4 |
| hypercenter | C43 | D67 |
| hypocenter | C67 | C4×#104 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ C43 | |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746536, C8×#14523971, #30746543, … |
| maximal normal subgroup of | #30746536, C8×#14523971, #30746543, … |
| maximal quotient of | C4×#16863125, C4×#16863128, #30746444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4316);