Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D1108 |
| Fitting | C4×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | C4×Q8×C277 | C2 |
| prime radical | C2×D1108 | C22 |
| hypercenter | C4×Q8 | D277 |
| hypocenter | C277 | D4×Q8 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
2785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982268, #47982272, #47982330, … |
| maximal normal subgroup of | #47982268, #47982272, #47982330, … |
| maximal quotient of | Q8×#17984540, C4⋊C4×D1108, Q8×C4⋊Dic277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1216);