Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | #124×D277 |
| Fitting | #124×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×#124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | #124×C277 | C2 |
| prime radical | C2×D4×D277 | C2 |
| hypercenter | #124 | D277 |
| hypocenter | C277 | C2×#124 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ #124 | |
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4432 |
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #329×D277, #47981763, #47981789, … |
| maximal normal subgroup of | #329×D277, #47981763, #47981789, … |
| maximal quotient of | #382×D277, #388×D277, #390×D277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1063);