Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C19×#125 ⋊ C2 |
| Sylow | C19 ⋊ #488 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^18,g^b=g^18,g^c=g^18148 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#488, C2×#11926901, #14573956, … |
| maximal normal subgroup of | D19×#488, C2×#11926901, #14573956, … |
| maximal quotient of | #14563765, #14564310, #14564317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 906);