Finite Group DatabasebetaFinite Group Databasebeta| order | 33524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C172×C29 ⋊ C4 |
| Sylow | C172 ⋊ Dic29 |
| Sylow | C29 ⋊ #11923883 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C172×C29 | C4 |
| prime radical, cosocle | C29×C17⋊D17 | C2 |
| LCS | G ▷ C172×C29 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8381 |
Polycyclic presentation:
2^2,17^2,29|a^2=b,c^a=c^13,d^a=d^13,e^a=e^28,c^b=c^16,d^b=d^162120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33524, 42);