Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C277 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #11764308 |
| commutator, hypocenter | C277 | C4×C16 |
| Frattini | C2×C4 | C2×#11764308 |
| Fitting | C2×C8×C277 | C4 |
| socle, prime radical | C22×C277 | C2×C8 |
| cosocle | C2×#14555660 | C22 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^217,g^b=g^276,g^c=g^2761168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1435);