Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊#64418 |
| Fitting, socle, Hall | C72×C37 ⋊ D3 |
| derived, Hall | C37×#3862 ⋊ C2 |
| Hall | #3862 ⋊ D37 |
| Sylow | C72 ⋊ D111 |
| Sylow | C37 ⋊ #64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C37×#3862 | C2 |
| Fitting, socle | C72×C37 | D3 |
| LCS | G ▷ C37×#3862 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,37,7^2|b^a=b^2,c^a=c^36,d^a=d^2e^3,e^a=d^6e^5,d^b=d^4e^4,e^b=e^2362 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊D37, #36344303, D37×#64418, … |
| maximal normal subgroup of | #64418⋊D37, #36344303, D37×#64418, … |
| maximal quotient of | #36344279, C2×C37⋊#64418, C37⋊#11725071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 80);