Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C37 ⋊ C2 |
| Sylow | C37 ⋊ #418 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^36,c^b=cf,d^b=df,g^b=g^36382 conjugacy classes — view the full character table.
| maximal subgroup of | #17994565, #17994567, #17994970, … |
| maximal normal subgroup of | #17994565, #17994567, #17994970, … |
| maximal quotient of | #17992988, #17993014, #17993040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 555);