Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q16×C37 ⋊ C2 |
| Sylow | C37 ⋊ #495 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|b^2=d,c^2=ef,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^36,g^b=g^36,g^c=g^36274 conjugacy classes — view the full character table.
| maximal subgroup of | #17996653, #17996654, #17996660, … |
| maximal normal subgroup of | #17996653, #17996654, #17996660, … |
| maximal quotient of | #17994189, #17994190, #17994199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 934);