Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C281 ⋊ C2 |
| Sylow | C281 ⋊ #525 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D281 |
| commutator, socle, cosocle | C22×C281 | C24 |
| Fitting | C22⋊Q8×C281 | C2 |
| hypercenter | C22⋊Q8 | D281 |
| hypocenter | C281 | #525 |
| LCS | G ▷ C22×C281 ▷ C281 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^6,281|d^2=e,b^a=be,c^a=cf,g^a=g^280,g^b=g^280,g^d=g^2801988 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49093793, #49093806, #49093845, … |
| maximal normal subgroup of | #49093793, #49093806, #49093845, … |
| maximal quotient of | #49097685, #49097739, #49097741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 1062);