Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ Q32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #64525 |
| commutator, cosocle | C8×C19 | C22 |
| Frattini | C8 | C2×D19 |
| Fitting | Q16×C19 | C2 |
| socle, prime radical | C2×C19 | D8 |
| hypercenter | Q16 | D19 |
| hypocenter | C19 | Q32 |
| LCS | G ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^5,19|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^18,c^b=cd,d^b=de74 conjugacy classes — view the full character table.
| maximal subgroup of | Q32×D19, C2×#10597286, #11926974, … |
| maximal normal subgroup of | Q32×D19, C2×#10597286, #11926974, … |
| maximal quotient of | #11926347, #11926348, #11926369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 35);