Finite Group DatabasebetaFinite Group Databasebeta| order | 31300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C313 ⋊ C4 |
| Sylow | C313 ⋊ #1044 |
| Sylow | C52 ⋊ Dic313 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C313 | C4 |
| prime radical, cosocle | C5⋊D5×C313 | C2 |
| LCS | G ▷ C52×C313 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3130 |
Polycyclic presentation:
2^2,5^2,313|a^2=b,c^a=c^2,d^a=d^3,e^a=e^312,c^b=c^4,d^b=d^42194 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31300, 45);