Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C37×C49 ⋊ C2×C3 |
| Hall | #19129580 ⋊ C2 |
| Hall | C49×D37 ⋊ C3 |
| Hall | D37 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ C2×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C37×C49 | C2×C3 |
| Frattini | C7 | #13095532 |
| socle | C7×C37 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,37,7|c^7=e^2,d^a=d^36,c^b=c^2e,d^b=d^10,e^b=e^2332 conjugacy classes — view the full character table.
| maximal subgroup of | #36344175, #24925915⋊C2, #36344181, … |
| maximal normal subgroup of | #36344175, #24925915⋊C2, #36344181, … |
| maximal quotient of | #36344154, C2×#24925915, #45657227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 7);