Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D19 |
| commutator, socle | C2×C19 | C23×C4 |
| Fitting | C2×M16×C19 | C2 |
| prime radical | C2×#64541 | C2 |
| cosocle | C4×C19 | C24 |
| hypercenter | C2×M16 | D19 |
| hypocenter | C19 | #568 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^18214 conjugacy classes — view the full character table.
| maximal subgroup of | #14563853, #14563856, #14563872, … |
| maximal normal subgroup of | #14563853, #14563856, #14563872, … |
| maximal quotient of | #14572052, #14572053, #14572060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1315);