Finite Group DatabasebetaFinite Group Databasebeta| order | 27584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4⋊Q8×C431 ⋊ C2 |
| Sylow | C431 ⋊ #541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D431 |
| commutator, socle, cosocle | C22×C431 | C24 |
| Fitting | C4⋊Q8×C431 | C2 |
| prime radical | C22×D431 | C23 |
| hypercenter | C4⋊Q8 | D431 |
| hypocenter | C431 | #541 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13792 |
Polycyclic presentation:
2^6,431|a^2=e,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^430,g^c=g^4303032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27584, 1160);