Finite Group DatabasebetaFinite Group Databasebeta| order | 8836 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C47 |
| direct product | C2×C47⋊D47 |
| unambiguous semidirect product | (C2×C47)⋊D47 |
| Fitting, socle | C2×C472 ⋊ C2 |
| derived, Sylow | C472 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C47⋊D47 |
| commutator, hypocenter | C472 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C472 | C2 |
| LCS | G ▷ C472 | |
| UCS | C1 ◁ C2 | |
250 conjugacy classes of subgroups.
2212 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×(C47⋊D47)⋊C3, D3×C47⋊D47, C2×C3×C47⋊D47, … |
| maximal normal subgroup of | C2×(C47⋊D47)⋊C3, C2×C3×C47⋊D47 |
| maximal quotient of | D3×C47⋊D47, C2×C3×C47⋊D47, C2×C3⋊(C47⋊D47) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8836, 12);