Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×C4⋊C8 ⋊ C2 |
| Sylow | C19 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=e,e^2=f,b^a=bd,g^b=g^18,g^c=g^18220 conjugacy classes — view the full character table.
| maximal subgroup of | #14562427, #14562429, #14562432, … |
| maximal normal subgroup of | #14562427, #14562429, #14562432, … |
| maximal quotient of | #14562429, #14562434, #14562441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 614);