Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C277 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D277 |
| commutator, socle, cosocle | C23×C277 | C23 |
| Fitting, prime radical | C22×D4×C277 | C2 |
| hypercenter | C22×D4 | D277 |
| hypocenter | C277 | #394 |
| LCS | G ▷ C23×C277 ▷ C277 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2762782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982093, #47982095, #47982100, … |
| maximal normal subgroup of | #47982093, #47982095, #47982100, … |
| maximal quotient of | #47981408, #47981410, #47981414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 463);