Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1201 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #23751199 |
| commutator, hypocenter | C1201 | C16 |
| Fitting, socle, prime radical | C2×C1201 | C8 |
| cosocle | #23751197 | C2 |
| LCS | G ▷ C1201 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19216 |
Polycyclic presentation:
2^4,1201|a^2=b,b^2=c,c^2=d,e^a=e^343,e^b=e^1152,e^c=e^1200316 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34063535, #50307949, #50307950, … |
| maximal normal subgroup of | C2×#34063535, #50307949, #50307950, … |
| maximal quotient of | #50307944, C2×#34063535 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 52);