Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C13×C25 | C3×C4 |
| Frattini | C5 | #19129750 |
| socle | C5×C7×C13 | C3×AGL(1,𝔽5) |
| prime radical | C7×C13⋊C3×D25 | C2 |
| cosocle | C7×C13×D25 | C2×C3 |
| LCS | G ▷ C7×C13×C25 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2275 |
Polycyclic presentation:
2,3,2,5,7,13,5|a^2=c,d^5=g,d^a=d^2g,e^a=e^6,f^a=f^12,g^a=g^2,f^b=f^3,d^c=d^4g^4,g^c=g^4352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 92);