Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C107 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D107 |
| commutator | C2×C107 | C2×C42 |
| Fitting | C2×M16×C107 | C2 |
| socle | C22×C107 | C22×C4 |
| hypercenter | C2×M16 | D107 |
| hypocenter | C107 | #405 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,b^2=e,d^2=f,g^a=g^106,c^b=cf,g^b=g^1061100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28336215, #28336217, #28336260, … |
| maximal normal subgroup of | #28336215, #28336217, #28336260, … |
| maximal quotient of | M16×C107⋊C8, #28334745, #28334748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 507);