Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #547 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C2×C4⋊C4×C31 | C2 |
| hypercenter | C2×C4⋊C4 | D31 |
| hypocenter | C31 | #547 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 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,c^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^30325 conjugacy classes — view the full character table.
| maximal subgroup of | #16857520, #16857522, #16857572, … |
| maximal normal subgroup of | #16857520, #16857522, #16857572, … |
| maximal quotient of | #16848538, #16848576, #16848580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1200);