Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×#107 ⋊ C2 |
| Sylow | C19 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^18,g^c=g^18148 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#428, C2×#11926585, #14572222, … |
| maximal normal subgroup of | D19×#428, C2×#11926585, #14572222, … |
| maximal quotient of | #14562386, #14562401, #14562419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 590);