Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #95×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1442 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6157 |
| commutator, socle | C23×C53 | C22×C4 |
| Fitting | #95×C53 | C4 |
| hypercenter | #95 | #6157 |
| hypocenter | C53 | #1442 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #95 | |
520 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=g,b^2=e,c^2=d,b^a=bd,c^a=ce,h^a=h^30,c^b=cf,h^g=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28303733, #28303735, #28303736, … |
| maximal normal subgroup of | #28303733, #28303735, #28303736, … |
| maximal quotient of | #28299401, #28299403, #28307573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19696);