Finite Group DatabasebetaFinite Group Databasebeta| order | 30608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C1913 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #21440083 |
| commutator, hypocenter | C1913 | C2×C8 |
| Frattini | C2 | C2×#21440083 |
| Fitting | C4×C1913 | C4 |
| socle | C2×C1913 | C2×C4 |
| prime radical | C2×D1913 | C4 |
| cosocle | Dic1913 | C22 |
| LCS | G ▷ C1913 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15304 |
Polycyclic presentation:
2^4,1913|a^2=c,c^2=d,e^a=e^712,e^b=e^1912,e^c=e^19121928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30608, 48);