Finite Group DatabasebetaFinite Group Databasebeta| order | 23212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#15693280 |
| Fitting, socle, derived, Hall | C7×C829 ⋊ C4 |
| Sylow | C829 ⋊ Dic7 |
| Sylow | C7 ⋊ #15693280 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C829 | C4 |
| prime radical, cosocle | C7×D829 | C2 |
| LCS | G ▷ C7×C829 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5803 |
Polycyclic presentation:
2^2,7,829|a^2=b,c^a=c^6,d^a=d^246,d^b=d^8281459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23212, 7);