Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ #400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D277 |
| commutator, socle, prime radical, cosocle | C23×C277 | C23 |
| Fitting | #95×C277 | C2 |
| hypercenter | #95 | D277 |
| hypocenter | C277 | #400 |
| LCS | G ▷ C23×C277 ▷ C277 | |
| UCS | C1 ◁ C23 ◁ #95 | |
134 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=de,c^2=d,b^a=bd,c^a=ce,g^a=g^276,c^b=cf,g^c=g^2762782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #400×D277, C2×#31799944, #47986423, … |
| maximal normal subgroup of | #400×D277, C2×#31799944, #47986423, … |
| maximal quotient of | #47981419, #47981423, #47981424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 491);