Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C337 ⋊ C2 |
| Sylow | C337 ⋊ #135 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^336,d^b=de,f^b=f^3362702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341111, #36341113, #36341114, … |
| maximal normal subgroup of | #36341111, #36341113, #36341114, … |
| maximal quotient of | #36341302, #36341343, C4×D2696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 168);