Finite Group DatabasebetaFinite Group Databasebeta| order | 14413 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C29×C71 ⋊ C7 |
| Sylow | C71 ⋊ C29⋊C7 |
| Sylow | C29 ⋊ C71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C71 | C7 |
| LCS | G ▷ C29×C71 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2059 |
Polycyclic presentation:
7,29,71|b^a=b^25,c^a=c^20301 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#28385698, #43273756, #43273764, … |
| maximal normal subgroup of | C2×#28385698, #43273756, #43273764, … |
| maximal quotient of | C2×#28385698 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14413, 8);