Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×H(5,𝔽2) ⋊ C2 |
| Sylow | C19 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^6,19|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^18,d^b=df,e^b=ef,d^c=df169 conjugacy classes — view the full character table.
| maximal subgroup of | #14565617, #14565629, #14565639, … |
| maximal normal subgroup of | #14565617, #14565629, #14565639, … |
| maximal quotient of | #14562553, #14562558, #14562581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 717);