Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D107 |
| Fitting | C4×Q8×C107 ⋊ C2 |
| Sylow | C107 ⋊ C2×C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D107 |
| commutator | C2×C107 | C23×C4 |
| Frattini | C22 | C23×D107 |
| Fitting | C4×Q8×C107 | C2 |
| socle | C22×C107 | C24 |
| hypercenter | C4×Q8 | D107 |
| hypocenter | C107 | C2×C4×Q8 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
298 conjugacy classes of subgroups.
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D107, #28334854, #28334888, … |
| maximal normal subgroup of | Q8⋊C8×D107, #28334854, #28334888, … |
| maximal quotient of | C4×C4⋊C4×D107, C4×#16812074, C4×Q8×Dic107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 1012);