Finite Group DatabasebetaFinite Group Databasebeta| order | 10376 |
| automorphism | Aut(G) order 13447296 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5188 |
| unambiguous semidirect product | C4⋊D1297 |
| Fitting | C4×C1297 ⋊ C2 |
| Sylow | C1297 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1297 |
| commutator, socle, cosocle | C2×C1297 | C22 |
| Fitting | C4×C1297 | C2 |
| hypercenter | C4 | D1297 |
| hypocenter | C1297 | D4 |
| LCS | G ▷ C2×C1297 ▷ C1297 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1297|b^a=bc,d^a=d^1296,d^b=d^12962597 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35209240, D10376, #35209242, … |
| maximal normal subgroup of | #35209240, D10376, #35209242, … |
| maximal quotient of | #35209232, C4⋊Dic1297, D10376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10376, 10);