Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11719945 |
| Fitting | C2×C4×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C25 |
| Frattini | C22 | C24×D53 |
| Fitting | C2×C4×Q8×C53 | C2 |
| hypercenter | C2×C4×Q8 | D53 |
| hypocenter | C53 | Q8×#41 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
1068 conjugacy classes of subgroups.
1090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27276133, #27276137, #27350966, … |
| maximal normal subgroup of | #27276133, #27276137, #27350966, … |
| maximal quotient of | C4⋊C4×#11719945, Q8×#13133174, Q8×#13133176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 18091);