Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D19 |
| commutator, socle, cosocle | C22×C19 | C23 |
| Fitting | C22⋊C4×C19 | C2 |
| prime radical | C2×C22⋊D19 | C2 |
| hypercenter | C22⋊C4 | D19 |
| hypocenter | C19 | #124 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^5,19|b^2=d,b^a=be,c^a=cde,f^a=f^18,c^b=ce104 conjugacy classes — view the full character table.
| maximal subgroup of | #124×D19, C2×#10597331, #11927071, … |
| maximal normal subgroup of | #124×D19, C2×#10597331, #11927071, … |
| maximal quotient of | #11926408, #11926432, #11926433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 80);