Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^5,19|b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^18,c^b=ce,d^c=de101 conjugacy classes — view the full character table.
| maximal subgroup of | #11926720, #11926721, #11926725, … |
| maximal normal subgroup of | #11926720, #11926721, #11926725, … |
| maximal quotient of | #11926543, #11926553, #11926584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 137);