Finite Group DatabasebetaFinite Group Databasebeta| order | 27372 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#22603650 |
| Fitting, socle, Hall | C3×C2281 ⋊ C4 |
| derived, Sylow | C2281 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #22603650 |
| commutator, hypocenter | C2281 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2281 | C4 |
| prime radical | C3×D2281 | C2 |
| cosocle | D2281 | C2×C3 |
| LCS | G ▷ C2281 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6843 |
1722 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27372, 10);