Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D19 |
| commutator, socle, prime radical | C22×C19 | C22×C4 |
| Fitting | C19×C4⋊C8 | C2 |
| cosocle | C2×C4×C19 | C23 |
| hypercenter | C4⋊C8 | D19 |
| hypocenter | C19 | #446 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^18,g^c=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#446, C2×#11926673, #14572564, … |
| maximal normal subgroup of | D19×#446, C2×#11926673, #14572564, … |
| maximal quotient of | #14563501, #14563508, #14563512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 678);