Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C7 |
| direct product | C2×C37×#3862 |
| Fitting, socle, Hall | C2×C72×C37 ⋊ C3 |
| derived, Sylow | C72 ⋊ C2×C3×C37 |
| Hall | C72×C37 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | #3862 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C37 | |
40 conjugacy classes of subgroups.
1406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#10596875, #36344246, C37×#10596872, … |
| maximal normal subgroup of | C37×#10596875, #36344246, C37×#10596872, … |
| maximal quotient of | C4×C37×#3862, C22×C37×#3862, C2×C37×#89205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 82);