Finite Group DatabasebetaFinite Group Databasebeta| order | 19472 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1217 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1217 | C16 |
| prime radical | D1217 | C8 |
| cosocle | #23753595 | C2 |
| LCS | G ▷ C1217 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1217 |
Polycyclic presentation:
2^4,1217|a^2=b,b^2=c,c^2=d,e^a=e^737,e^b=e^387,e^c=e^78,e^d=e^121692 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19472, 54);