Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C7⋊#13049932) |
| unambiguous semidirect product | C7⋊(C3⋊#13049932) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C7×C13 | C4 |
| prime radical, cosocle | C3×C7×C13×C5⋊D5 | C2 |
| LCS | G ▷ C3×C52×C7×C13 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2730 |
Polycyclic presentation:
2^2,3,5^2,7,13|a^2=b,c^a=c^2,d^a=d^2,e^a=e^3,f^a=f^6,g^a=g^12,d^b=d^4,e^b=e^41914 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 962);