Finite Group DatabasebetaFinite Group Databasebeta| order | 33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C397 ⋊ C3×C4 |
| Hall | C7×Dic397 ⋊ C3 |
| Hall | #22552380 ⋊ C4 |
| Hall | Dic397 ⋊ ΓL(1,𝔽8) |
| Sylow | C397 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ Dic397⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #30659823 |
| commutator, hypocenter | C7×C397 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C397 | C2×C3 |
| prime radical | C2×#22552380 | C2 |
| LCS | G ▷ C7×C397 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11116 |
Polycyclic presentation:
2,3,7,397,2|a^2=e,d^a=d^396,c^b=c^2,d^b=d^34944 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33348, 16);