Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D19 |
| commutator, socle, cosocle | C22×C19 | C23 |
| Fitting | C2×D4×C19 | C2 |
| hypercenter | C2×D4 | D19 |
| hypocenter | C19 | #121 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^5,19|b^a=be,c^a=cd,f^a=f^18,c^b=ce104 conjugacy classes — view the full character table.
| maximal subgroup of | #121×D19, C2×#10597385, #11927050, … |
| maximal normal subgroup of | #121×D19, C2×#10597385, #11927050, … |
| maximal quotient of | #11926402, #11926421, #11926424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 134);