Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C27900 |
| abelian | C4×C9×C25×C31 |
| multiplicative | (ℤ/27901)ˣ, (ℤ/55802)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C5 | C2×C3×C5×C31 |
| socle, prime radical | C2×C3×C5×C31 | C2×C3×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
54 conjugacy classes of subgroups.
27900 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic13950, D27900 |
| maximal subgroup of | Dic13950, D27900 |
| maximal normal subgroup of | Dic13950, D27900 |
| automorphism group of | C27901 |
| outer automorphism group of | C27901 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 1);