Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#16812019 |
| Sylow | C107 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D107 |
| commutator | C2×C107 | C2×C42 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | C22×C8×C107 | C2 |
| socle | C23×C107 | C2×C4 |
| hypercenter | C22×C8 | D107 |
| hypocenter | C107 | C2×#97 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
146 conjugacy classes of subgroups.
1736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334540, #28334544, #97×Dic107, … |
| maximal normal subgroup of | #28334540, #28334544, #97×Dic107, … |
| maximal quotient of | C2×#20292348, C2×#20292349, #28334750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 497);