Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13133817 |
| Fitting | C22×D4×C107 ⋊ C2 |
| Sylow | C107 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D107 |
| commutator | C2×C107 | C25 |
| Frattini | C2 | C24×D107 |
| Fitting | C22×D4×C107 | C2 |
| socle | C23×C107 | C23 |
| hypercenter | C22×D4 | D107 |
| hypocenter | C107 | C22×#41 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28336377, #28336386, #28336398, … |
| maximal normal subgroup of | #28336377, #28336386, #28336398, … |
| maximal quotient of | C22×#16812065, C22×#16812067, C22×(C22⋊D107)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 1375);