Finite Group DatabasebetaFinite Group Databasebeta| order | 33180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #15693306⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C79 | C22×C3 |
| LCS | G ▷ C5×C7×C79 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2765 |
Polycyclic presentation:
2^2,3,5,7,79|e^a=e^6,f^a=f^78,d^b=d^4,e^b=e^6,e^c=e^2,f^c=f^23275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33180, 79);