Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C112×C13 ⋊ C4 |
| Hall | C112×C13 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ #261 |
| Sylow | C112 ⋊ #63122 |
| Hall | C5×C13 ⋊ #92150 |
| Sylow | C13 ⋊ #14559097 |
| Sylow | C5 ⋊ #20262573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C112×C13 | C4 |
| prime radical, cosocle | C5⋊(C11⋊D143) | C2 |
| LCS | G ▷ C5×C112×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
Polycyclic presentation:
2^2,5,11^2,13|a^2=b,c^a=c^2,d^a=d^8e^8,e^a=d^7e^3,f^a=f^5,c^b=c^4,d^b=d^10,e^b=e^10,f^b=f^121970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 181);