Finite Group DatabasebetaFinite Group Databasebeta| order | 13780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C13×C53 ⋊ C4 |
| Hall | C13×C53 ⋊ AGL(1,𝔽5) |
| Hall | C5×C53 ⋊ #261 |
| Hall | C5×C13 ⋊ Dic53 |
| Sylow | C53 ⋊ #63121 |
| Sylow | C13 ⋊ #11761507 |
| Sylow | C5 ⋊ #14583754 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C53 | C4 |
| prime radical, cosocle | C53×D65 | C2 |
| LCS | G ▷ C5×C13×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3445 |
Polycyclic presentation:
2^2,5,13,53|a^2=b,c^a=c^2,d^a=d^8,e^a=e^52,c^b=c^4,d^b=d^12904 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13780, 43);