Finite Group DatabasebetaFinite Group Databasebeta| order | 31588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C53×C149 ⋊ C4 |
| Sylow | C149 ⋊ #6157 |
| Sylow | C53 ⋊ Dic149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53×C149 | C4 |
| prime radical, cosocle | D53×C149 | C2 |
| LCS | G ▷ C53×C149 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7897 |
Polycyclic presentation:
2^2,53,149|a^2=b,c^a=c^30,d^a=d^148,c^b=c^522089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31588, 10);