Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^5,37|a^2=d,d^2=e,b^a=bc,f^b=f^36308 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C8×D37, C2×#11924448, #14557495, … |
| maximal normal subgroup of | C22⋊C8×D37, C2×#11924448, #14557495, … |
| maximal quotient of | #14557256, #14557258, #14557260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 58);