Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #436 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^36,c^b=cf,g^b=g^36604 conjugacy classes — view the full character table.
| maximal subgroup of | #17992553, #17992555, #17993425, … |
| maximal normal subgroup of | #17992553, #17992555, #17993425, … |
| maximal quotient of | #17993482, #17993488, #17993494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 628);