Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #97×C107 ⋊ C2 |
| Sylow | C107 ⋊ #489 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D428 |
| commutator | C2×C4×C107 | C23 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | #97×C107 | C2 |
| socle | C22×C107 | C2×D4 |
| hypercenter | #97 | D107 |
| hypocenter | C107 | #489 |
| LCS | G ▷ C2×C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^106,c^b=cf1076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28335768, #28335769, #28335779, … |
| maximal normal subgroup of | #28335768, #28335769, #28335779, … |
| maximal quotient of | #28336595, #28337151, #28337158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 909);