Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C107 ⋊ C2 |
| Sylow | C107 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D107 |
| commutator | C2×C107 | C22×C8 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | C4×C8×C107 | C2 |
| socle | C22×C107 | C22×C4 |
| hypercenter | C4×C8 | D107 |
| hypocenter | C107 | #431 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^1061736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13133801, #28334740, #28334743, … |
| maximal normal subgroup of | C8×#13133801, #28334740, #28334743, … |
| maximal quotient of | #28336206, C4×(C2×D107)⋊C8, C4×Dic107⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 600);