Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^36616 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#10596929, #17992875, #17992878, … |
| maximal normal subgroup of | C8×#10596929, #17992875, #17992878, … |
| maximal quotient of | #17994341, C4×#11924448, C4×#11924465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 600);