Finite Group DatabasebetaFinite Group Databasebeta| order | 28900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C172×C25 ⋊ C4 |
| Sylow | C172 ⋊ Dic25 |
| Sylow | C25 ⋊ #11923885 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C172×C25 | C4 |
| Frattini | C5 | #19153622 |
| socle | C5×C172 | Dic5 |
| prime radical | C5×C17×D17 | D5 |
| cosocle | C17×C25×D17 | C2 |
| LCS | G ▷ C172×C25 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1700 |
Polycyclic presentation:
2^2,5,17^2,5|a^2=b,c^5=f^4,c^a=c^4f,d^a=d^13,e^a=e^16,f^a=f^4,d^b=d^162128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28900, 77);