Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C107 ⋊ #398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D107 |
| commutator, socle | C23×C107 | C23 |
| Fitting | #95×C107 | C2 |
| hypercenter | #95 | D107 |
| hypocenter | C107 | #398 |
| LCS | G ▷ C23×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ #95 | |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^106,g^c=g^1061082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28335459, #28335461, #28335465, … |
| maximal normal subgroup of | #28335459, #28335461, #28335465, … |
| maximal quotient of | #28334713, #28334715, #28334717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 481);