Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #520 |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^36,g^c=g^36,g^d=g^36394 conjugacy classes — view the full character table.
| maximal subgroup of | #18003423, #18003427, #18003434, … |
| maximal normal subgroup of | #18003423, #18003427, #18003434, … |
| maximal quotient of | #17996950, #17996956, #17996961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1031);