Finite Group DatabasebetaFinite Group Databasebeta| order | 30604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1093⋊C7 |
| derived, Sylow | C1093 ⋊ C4×C7 |
| Hall | C1093⋊C7 ⋊ C4 |
| Hall | Dic1093 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1093⋊C7 |
| commutator, hypocenter | C1093 | C4×C7 |
| Fitting, socle, cosocle | C2×C1093 | C2×C7 |
| prime radical | C2×C1093⋊C7 | C2 |
| LCS | G ▷ C1093 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4372 |
Polycyclic presentation:
2,7,1093,2|a^2=d,c^a=c^1092,c^b=c^9184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30604, 2);