Finite Group DatabasebetaFinite Group Databasebeta| order | 27993 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C31×C43 ⋊ C3 |
| Hall | C31×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C43 ⋊ C31⋊C3 |
| Hall | C7×C31 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ #10620253 |
| Sylow | C31 ⋊ #11744749 |
| Sylow | C7 ⋊ #16860687 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C31×C43 | C3 |
| LCS | G ▷ C7×C31×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9331 |
Polycyclic presentation:
3,7,31,43|b^a=b^2,c^a=c^25,d^a=d^363113 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27993, 11);