Finite Group DatabasebetaFinite Group Databasebeta| order | 38612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic1379 |
| derived, Hall | C72×C197 ⋊ C4 |
| Sylow | C197 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic197 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊D1379 |
| commutator, hypocenter | C72×C197 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C72×C197 | C2 |
| LCS | G ▷ C72×C197 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,197,2|a^2=e,b^a=b^6,c^a=c^6,d^a=d^1969656 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38612, 24);