Finite Group DatabasebetaFinite Group Databasebeta| order | 5380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C269 ⋊ C4 |
| Sylow | C269 ⋊ Dic5 |
| Sylow | C5 ⋊ #11761640 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C269 | C4 |
| LCS | G ▷ C5×C269 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,269|a^2=b,c^a=c^4,d^a=d^82,d^b=d^268343 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19129043, C3⋊#19129043, #41001955, … |
| maximal normal subgroup of | C3×#19129043, C5×#19129043, C7×#19129043 |
| maximal quotient of | C3×#19129043, C3⋊#19129043, #41001955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5380, 11);