Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #97×C107 ⋊ C2 |
| Sylow | C107 ⋊ #440 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D428 |
| commutator | C4×C107 | C22×C4 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | #97×C107 | C2 |
| socle | C22×C107 | C2×D4 |
| hypercenter | #97 | D107 |
| hypocenter | C107 | #440 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,107|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^106,d^b=df,g^b=g^1061082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #440×D107, C2×#20292729, #28345256, … |
| maximal normal subgroup of | #440×D107, C2×#20292729, #28345256, … |
| maximal quotient of | #28335275, #28335320, #28335341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 651);