Finite Group DatabasebetaFinite Group Databasebeta| order | 11504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C719⋊C8 |
| unambiguous semidirect product | (C2×C719)⋊C8 |
| derived, Sylow | C719 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D719 |
| commutator, hypocenter | C719 | C2×C8 |
| Frattini | C4 | C2×D719 |
| Fitting | C2×C4×C719 | C2 |
| socle, prime radical | C22×C719 | C4 |
| cosocle | C4×C719 | C22 |
| LCS | G ▷ C719 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
2888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic719, C4×C719⋊C8, #37527504, … |
| maximal normal subgroup of | C8×Dic719, C4×C719⋊C8, #37527504, … |
| maximal quotient of | C4×C719⋊C8, C22⋊(C719⋊C8), C4⋊(C719⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11504, 22);