Finite Group DatabasebetaFinite Group Databasebeta| order | 33411 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C37×C43 ⋊ C3 |
| Hall | C37×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C43 ⋊ C37⋊C3 |
| Hall | C7×C37 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ #11715913 |
| Sylow | C37 ⋊ #11744748 |
| Sylow | C7 ⋊ #18012031 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C37×C43 | C3 |
| LCS | G ▷ C7×C37×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11137 |
Polycyclic presentation:
3,7,37,43|b^a=b^2,c^a=c^26,d^a=d^63715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33411, 12);