Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#11744607 |
| derived, Hall | C52⋊C9 ⋊ C4×C31 |
| Hall | C31×C52⋊C9 ⋊ C4 |
| Hall | C52×C31 ⋊ Dic9 |
| Sylow | C52 ⋊ C31×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | #90646 |
| commutator, hypocenter | C52⋊C9 | C4×C31 |
| Frattini | C2×C3 | C31×#3874 |
| Fitting, socle, prime radical | C2×C3×C52×C31 | D3 |
| cosocle | C2×C52⋊C9 | C2×C31 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C2×C31 | |
60 conjugacy classes of subgroups.
1488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 103);