Finite Group DatabasebetaFinite Group Databasebeta| order | 30044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#16864282 |
| Fitting, socle, derived, Hall | C7×C29×C37 ⋊ C4 |
| Hall | C29×C37 ⋊ Dic7 |
| Hall | C7×C37 ⋊ #1181 |
| Hall | C7×C29 ⋊ Dic37 |
| Sylow | C37 ⋊ C7⋊#1181 |
| Sylow | C29 ⋊ Dic259 |
| Sylow | C7 ⋊ #16864282 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C29×C37 | C4 |
| prime radical, cosocle | C7×C37×D29 | C2 |
| LCS | G ▷ C7×C29×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7511 |
Polycyclic presentation:
2^2,7,29,37|a^2=b,c^a=c^6,d^a=d^17,e^a=e^36,d^b=d^282075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30044, 37);