Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C277 ⋊ C2 |
| Sylow | C277 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D277 |
| commutator, socle, cosocle | C23×C277 | C23 |
| Fitting | #95×C277 | C2 |
| prime radical | C22×D1108 | C2 |
| hypercenter | #95 | D277 |
| hypocenter | C277 | #394 |
| LCS | G ▷ C23×C277 ▷ C277 | |
| UCS | C1 ◁ C23 ◁ #95 | |
238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 61 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,g^a=g^276,c^b=cf,g^b=g^276,g^c=g^2762782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982097, #47982099, #47982103, … |
| maximal normal subgroup of | #47982097, #47982099, #47982103, … |
| maximal quotient of | #47981407, #47981411, #47981415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 467);