Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#64438 |
| Sylow | C37 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^5,37|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^31,f^d=f^3692 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#64438, #14558381, Q8⋊#64438, … |
| maximal normal subgroup of | D4⋊#64438, #14558381, Q8⋊#64438, … |
| maximal quotient of | #14558394, #14558396, #14558399, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 212);