Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10587739 |
| commutator | C2×C137 | C2×C42 |
| Fitting | C4⋊C4×C137 | C4 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C4⋊C4 | #10587739 |
| hypocenter | C137 | #405 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,g^a=g^100,c^b=cf,g^c=g^136,g^d=g^136380 conjugacy classes — view the full character table.
| maximal subgroup of | #31796564, #31796566, #31796568, … |
| maximal normal subgroup of | #31796564, #31796566, #31796568, … |
| maximal quotient of | #31795991, #31795995, #31796001, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1514);