Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C107 ⋊ #563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D107 |
| commutator, socle | C22×C107 | C24 |
| Fitting | #124×C107 | C2 |
| hypercenter | #124 | D107 |
| hypocenter | C107 | #563 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #124 | |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=e,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^c=g^106761 conjugacy classes — view the full character table.
| maximal subgroup of | #28335757, #28335760, #28335770, … |
| maximal normal subgroup of | #28335757, #28335760, #28335770, … |
| maximal quotient of | #28339611, #28339621, #28339635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 1299);