Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C19 ⋊ C2 |
| Sylow | C19 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D19 |
| commutator, cosocle | C4×C19 | C23 |
| Frattini | C4 | C22×D19 |
| Fitting | #41×C19 | C2 |
| socle | C2×C19 | C2×D4 |
| hypercenter | #41 | D19 |
| hypocenter | C19 | #135 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^5,19|b^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^18,d^c=de104 conjugacy classes — view the full character table.
| maximal subgroup of | #11926658, #11926659, #11926663, … |
| maximal normal subgroup of | #11926658, #11926659, #11926663, … |
| maximal quotient of | #11926538, #11926540, #11926580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 145);