Finite Group DatabasebetaFinite Group Databasebeta| order | 1164 |
| isoclinism | isoclinic class of #87604⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #87604⋊C3 |
| Fitting, socle, derived, Sylow | C97 ⋊ C3×C4 |
| Hall | #87604 ⋊ C3 |
| Hall | C97⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C97 | C3×C4 |
| prime radical | D97⋊C3 | C2 |
| cosocle | D97 | C2×C3 |
| LCS | G ▷ C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 97 |
Polycyclic presentation:
2,3,2,97|a^2=c,d^a=d^22,d^b=d^61,d^c=d^9620 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#87604⋊C3, C3⋊(#87604⋊C3), C11×#87604⋊C3, … |
| maximal normal subgroup of | C3×#87604⋊C3, C11×#87604⋊C3, C13×#87604⋊C3, … |
| maximal quotient of | #87604⋊C9, C3×#87604⋊C3, C3⋊(#87604⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1164, 7);