Finite Group DatabasebetaFinite Group Databasebeta| order | 10072 |
| automorphism | Aut(G) order 12670576 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5036 |
| unambiguous semidirect product | C4⋊D1259 |
| Fitting | C4×C1259 ⋊ C2 |
| Sylow | C1259 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1259 |
| commutator, socle, cosocle | C2×C1259 | C22 |
| Fitting | C4×C1259 | C2 |
| hypercenter | C4 | D1259 |
| hypocenter | C1259 | D4 |
| LCS | G ▷ C2×C1259 ▷ C1259 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1259|b^a=bc,d^a=d^1258,d^b=d^12582521 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34117853, D10072, #34117855, … |
| maximal normal subgroup of | #34117853, D10072, #34117855, … |
| maximal quotient of | (C2×D1259)⋊C4, C4⋊Dic1259, D10072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10072, 10);