Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10587717⋊D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C13×C25 | C22×C3 |
| Frattini | C5 | #10587717⋊D5 |
| socle | C5×C7×C13 | C2×C3×D5 |
| LCS | G ▷ C7×C13×C25 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2275 |
Polycyclic presentation:
2^2,3,5,7,13,5|d^5=g^4,f^a=f^12,d^b=d^4g,e^b=e^6,g^b=g^4,e^c=e^2,f^c=f^9312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 99);