Finite Group DatabasebetaFinite Group Databasebeta| order | 16653 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13×C61 ⋊ C3 |
| Hall | C13×C61 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C61 ⋊ C13⋊C3 |
| Hall | C7×C13 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ #63271 |
| Sylow | C13 ⋊ #13046197 |
| Sylow | C7 ⋊ #14558651 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C61 | C3 |
| LCS | G ▷ C7×C13×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5551 |
Polycyclic presentation:
3,7,13,61|b^a=b^2,c^a=c^9,d^a=d^471853 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#30659353, #45686574, #45686587, … |
| maximal normal subgroup of | C2×#30659353, #45686574, #45686587, … |
| maximal quotient of | C2×#30659353 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16653, 13);