Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C31×C22⋊Q8 ⋊ C2 |
| Sylow | C31 ⋊ #554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×C22⋊Q8 | C2 |
| prime radical | C2×C22⋊D31 | C22 |
| hypercenter | C22⋊Q8 | D31 |
| hypocenter | C31 | #554 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^30,g^c=g^30235 conjugacy classes — view the full character table.
| maximal subgroup of | #16857528, #16857530, #16857580, … |
| maximal normal subgroup of | #16857528, #16857530, #16857580, … |
| maximal quotient of | #16848587, #16848590, #16848607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1257);