Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | (C37⋊C3)⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C2×C3 |
| Hall | C72×C37⋊C3 ⋊ C2 |
| Hall | C7⋊D259 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ C3×C7⋊D7 |
| 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.
Polycyclic presentation:
2,3,7^2,37|c^a=c^6,d^a=d^6,e^a=e^36,e^b=e^26372 conjugacy classes — view the full character table.
| maximal subgroup of | #36344309, D7×(C37⋊C3)⋊D7, C7⋊D7×D37⋊C3, … |
| maximal normal subgroup of | #36344309, D7×(C37⋊C3)⋊D7, C7⋊D7×D37⋊C3, … |
| maximal quotient of | #36344276, C2×(C37⋊C3)⋊(C7⋊D7), #66524⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 77);