Finite Group DatabasebetaFinite Group Databasebeta| order | 30592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C239 ⋊ #2351 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D239 |
| commutator | C22×C239 | C23×C4 |
| Fitting | #389×C239 | C2 |
| socle, prime radical, cosocle | C23×C239 | C24 |
| hypercenter | #389 | D239 |
| hypocenter | C239 | #2351 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C23 ◁ #389 | |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30592 |
Polycyclic presentation:
2^7,239|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^238,h^d=h^2383382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30592, 7429);