Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#22579926 |
| Fitting | C2×#41×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D277 |
| commutator, cosocle | C2×C277 | C25 |
| Frattini | C2 | C24×D277 |
| Fitting | C2×#41×C277 | C2 |
| socle | C22×C277 | C24 |
| hypercenter | C2×#41 | D277 |
| hypocenter | C277 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4432 |
2794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983119, #47983122, #47983135, … |
| maximal normal subgroup of | #47983119, #47983122, #47983135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1380);