Finite Group DatabasebetaFinite Group Databasebeta| order | 2964 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C19 ⋊ C3×C4 |
| Hall | C19×Dic13 ⋊ C3 |
| Hall | #10625202 ⋊ C4 |
| Hall | Dic13 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ Dic13⋊C3 |
| Sylow | C13 ⋊ C4×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #13093364 |
| commutator, hypocenter | C13×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C19 | C2×C3 |
| prime radical | C2×#10625202 | C2 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 988 |
Polycyclic presentation:
2,3,13,19,2|a^2=e,c^a=c^12,c^b=c^9,d^b=d^11112 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15688283, #28414757, #28414793, … |
| maximal normal subgroup of | C5×#15688283, C7×#15688283, C11×#15688283, … |
| maximal quotient of | C5×#15688283, #28414757, #28414793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2964, 10);