Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#423 ⋊ C2 |
| Sylow | C53 ⋊ #2925 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#423 | C2 |
| hypercenter | #423 | D53 |
| hypocenter | C53 | #2925 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #423 | |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^52,d^b=dg,h^b=h^52,d^c=dg,h^c=h^52778 conjugacy classes — view the full character table.
| maximal subgroup of | #27278396, #27278400, #27278410, … |
| maximal normal subgroup of | #27278396, #27278400, #27278410, … |
| maximal quotient of | #27381592, #27381646, #27382017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13178);