Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C42×C137 ⋊ C4 |
| Sylow | C137 ⋊ #376 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#10587739 |
| commutator | C2×C137 | C2×C42 |
| Frattini | C22 | C22×#10587739 |
| Fitting | C42×C137 | C4 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C42 | #10587739 |
| hypocenter | C137 | #376 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=f,c^2=d,b^a=bd,g^a=g^100,g^e=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795612, #31795676, #31795678, … |
| maximal normal subgroup of | #31795612, #31795676, #31795678, … |
| maximal quotient of | C4×(C2×#10587739)⋊C4, #31795964, #31795965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1485);