Finite Group DatabasebetaFinite Group Databasebeta| order | 33902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C23×C67 ⋊ C2×C11 |
| Hall | #30683988 ⋊ C2 |
| Hall | D1541 ⋊ C11 |
| Sylow | C67 ⋊ AGL(1,𝔽23) |
| Sylow | C23 ⋊ D67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C67 | C2×C11 |
| LCS | G ▷ C23×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1541 |
Polycyclic presentation:
2,11,23,67|c^a=c^22,d^a=d^66,c^b=c^2,d^b=d^6492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33902, 47);