Finite Group DatabasebetaFinite Group Databasebeta| order | 10376 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1297 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D1297 |
| commutator, hypocenter | C1297 | C8 |
| Fitting, cosocle | C4×C1297 | C2 |
| socle, prime radical | C2×C1297 | C4 |
| LCS | G ▷ C1297 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1297|a^2=b,b^2=c,d^a=d^12962600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D1297, C2×#23780640, #35209238, … |
| maximal normal subgroup of | C8×D1297, C2×#23780640, #35209238, … |
| maximal quotient of | #35209230, C2×#23780640 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10376, 6);