Finite Group DatabasebetaFinite Group Databasebeta| order | 25988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C73×C89 ⋊ C4 |
| Sylow | C89 ⋊ #64408 |
| Sylow | C73 ⋊ #67063 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73×C89 | C4 |
| prime radical, cosocle | D6497 | C2 |
| LCS | G ▷ C73×C89 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6497 |
Polycyclic presentation:
2^2,73,89|a^2=b,c^a=c^27,d^a=d^55,c^b=c^72,d^b=d^881628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25988, 8);