Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D37×#3861 |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C2×C3 |
| Hall | C37×#3861 ⋊ C2 |
| Hall | C72×D37 ⋊ C3 |
| Sylow | C72 ⋊ C3×D37 |
| Sylow | C37 ⋊ C2×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C37 | C2×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #3861×#3866, #36344364, D37×#64424, … |
| maximal normal subgroup of | #3861×#3866, #36344364, D37×#64424, … |
| maximal quotient of | #3861×Dic37, C2×D37×#3861, D37×#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 68);