Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #460 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^36,e^c=ef,g^c=g^36379 conjugacy classes — view the full character table.
| maximal subgroup of | #17993656, #17993657, #17993662, … |
| maximal normal subgroup of | #17993656, #17993657, #17993662, … |
| maximal quotient of | #17993945, #17993957, #17993967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 750);