Finite Group DatabasebetaFinite Group Databasebeta| order | 772 |
| isoclinism | isoclinic class of #11715871 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C193 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C193 | C4 |
| prime radical, cosocle | D193 | C2 |
| LCS | G ▷ C193 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 193 |
| transitive degree | μt(G) = 193 |
Polycyclic presentation:
2^2,193|a^2=b,c^a=c^112,c^b=c^19252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11715871, #13095402, #11715871⋊C3, … |
| maximal normal subgroup of | C2×#11715871, #13095402, #11715871⋊C3, … |
| maximal quotient of | #13095400, C2×#11715871, C3×#11715871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(772, 3);