Finite Group DatabasebetaFinite Group Databasebeta| order | 10132 |
| automorphism | Aut(G) order 11996288 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2533 |
| derived, Hall | C17×C149 ⋊ C4 |
| Sylow | C149 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2533 |
| commutator, hypocenter | C17×C149 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C17×C149 | C2 |
| LCS | G ▷ C17×C149 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,149,2|a^2=d,b^a=b^16,c^a=c^1482536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2533, Dic7599, Dic5066, … |
| maximal normal subgroup of | C3×Dic2533, Dic5066 |
| maximal quotient of | C3×Dic2533, Dic7599, Dic12665 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10132, 4);