Finite Group DatabasebetaFinite Group Databasebeta| order | 8405 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C412 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C5 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
5,41^2|b^a=b^10,c^a=c^18341 conjugacy classes — view the full character table.
| maximal subgroup of | #30681142, #30681143, #30681144, … |
| maximal normal subgroup of | #30681142, #30681143, #30681144, … |
| maximal quotient of | C2×#22554262, C3×#22554262 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8405, 5);