Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D53 |
| commutator | C2×C53 | C43 |
| Fitting | C53×#376 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | #376 | D53 |
| hypocenter | C53 | #1726 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^52,c^b=cg1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27274530, #27274534, #27274538, … |
| maximal normal subgroup of | #27274530, #27274534, #27274538, … |
| maximal quotient of | #27273446, #27273449, #27273455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4197);