Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#17984564 |
| Fitting | C22×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D277 |
| commutator, cosocle | C2×C277 | C25 |
| Frattini | C2 | C24×D277 |
| Fitting | C22×Q8×C277 | C2 |
| socle | C23×C277 | C23 |
| hypercenter | C22×Q8 | D277 |
| hypocenter | C277 | C22×#41 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983094, #47983106, #47985656, … |
| maximal normal subgroup of | #47983094, #47983106, #47985656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1377);