Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C13 ⋊ C4⋊C4 |
| Sylow | C13 ⋊ #683 |
| Sylow | C5 ⋊ #6101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5×D13 |
| commutator | C2×C5×C13 | C2×C4 |
| Fitting, socle, prime radical, cosocle | C22×C5×C13 | C22 |
| hypocenter | C5×C13 | C4⋊C4 |
| LCS | G ▷ C2×C5×C13 ▷ C5×C13 | |
| UCS | C1 ◁ C22 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1040 |
Polycyclic presentation:
2^4,5,13|a^2=d,b^2=d,b^a=bc,f^a=f^12,e^b=e^4122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 34);