Finite Group DatabasebetaFinite Group Databasebeta| order | 33580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13091735 |
| Fitting, socle, derived, Hall | C5×C23×C73 ⋊ C4 |
| Hall | C23×C73 ⋊ Dic5 |
| Hall | C5×C73 ⋊ Dic23 |
| Hall | C5×C23 ⋊ #64408 |
| Sylow | C73 ⋊ Dic115 |
| Sylow | C23 ⋊ #13091735 |
| Sylow | C5 ⋊ C23⋊#64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C23×C73 | C4 |
| prime radical, cosocle | C5×C23×D73 | C2 |
| LCS | G ▷ C5×C23×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8395 |
Polycyclic presentation:
2^2,5,23,73|a^2=b,c^a=c^4,d^a=d^22,e^a=e^27,e^b=e^722188 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33580, 23);