Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | M16×C137 ⋊ C4 |
| Sylow | C137 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#10587739 |
| commutator, socle | C2×C137 | C2×C42 |
| Fitting | M16×C137 | C4 |
| hypercenter | M16 | #10587739 |
| hypocenter | C137 | #405 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ M16 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,g^a=g^37,c^b=cf,g^b=g^100,g^d=g^136,g^e=g^136380 conjugacy classes — view the full character table.
| maximal subgroup of | #31796546, #31796548, #31796565, … |
| maximal normal subgroup of | #31796546, #31796548, #31796565, … |
| maximal quotient of | M16×#11764047, #31795987, #31795994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1515);