Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,e^2=f,b^a=bd,c^b=cf,g^b=g^36604 conjugacy classes — view the full character table.
| maximal subgroup of | #17992521, #17994546, #17994561, … |
| maximal normal subgroup of | #17992521, #17994546, #17994561, … |
| maximal quotient of | #17992942, #17992947, #17992951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 515);