Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#408 ⋊ C2 |
| Sylow | C53 ⋊ #2980 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#408 | C2 |
| hypercenter | #408 | D53 |
| hypocenter | C53 | #2980 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
394 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,d^b=dg,d^c=dg,h^c=h^52766 conjugacy classes — view the full character table.
| maximal subgroup of | #27300909, #27300912, #27300934, … |
| maximal normal subgroup of | #27300909, #27300912, #27300934, … |
| maximal quotient of | #27382816, #27382817, #27382854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13579);