Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C107 ⋊ #364 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D428 |
| commutator | C4×C107 | C2×C8 |
| Frattini | C2×C8 | C2×D107 |
| Fitting | C4×C8×C107 | C2 |
| socle | C2×C107 | C4⋊C8 |
| hypercenter | C4×C8 | D107 |
| hypocenter | C107 | #364 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^1061724 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334434, #28334435, #28334437, … |
| maximal normal subgroup of | #28334434, #28334435, #28334437, … |
| maximal quotient of | #28334525, #28334531, #28334543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 370);