Finite Group DatabasebetaFinite Group Databasebeta| order | 21308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#15690200 |
| Fitting, socle, derived, Hall | C7×C761 ⋊ C4 |
| Sylow | C761 ⋊ Dic7 |
| Sylow | C7 ⋊ #15690200 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C761 | C4 |
| prime radical, cosocle | C7×D761 | C2 |
| LCS | G ▷ C7×C761 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5327 |
Polycyclic presentation:
2^2,7,761|a^2=b,c^a=c^6,d^a=d^722,d^b=d^7601340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21308, 7);