Finite Group DatabasebetaFinite Group Databasebeta| order | 1164 |
| isoclinism | isoclinic class of C3⋊#87604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#87604 |
| Fitting, socle, derived, Hall | C3×C97 ⋊ C4 |
| Sylow | C97 ⋊ Dic3 |
| Sylow | C3 ⋊ #87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C97 | C4 |
| prime radical, cosocle | C3×D97 | C2 |
| LCS | G ▷ C3×C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 291 |
Polycyclic presentation:
2^2,3,97|a^2=b,c^a=c^2,d^a=d^22,d^b=d^9678 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#87604, C3⋊(#87604⋊C3), C3×C3⋊#87604, … |
| maximal normal subgroup of | C3⋊(#87604⋊C3), C3×C3⋊#87604, C11×C3⋊#87604, … |
| maximal quotient of | C9⋊#87604, C3×C3⋊#87604, C3⋊(C3⋊#87604), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1164, 10);