Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ #364 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^b=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #364×D37, C2×#14557353, #17996360, … |
| maximal normal subgroup of | #364×D37, C2×#14557353, #17996360, … |
| maximal quotient of | #17992659, #17992665, #17992677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 369);