Finite Group DatabasebetaFinite Group Databasebeta| order | 11504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic719 |
| derived, Sylow | C719 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D719 |
| commutator, hypocenter | C719 | C22×C4 |
| Frattini | C2 | C22×D719 |
| Fitting, socle, prime radical | C23×C719 | C2 |
| cosocle | C2×C719 | C23 |
| LCS | G ▷ C719 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
2888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C719⋊#95, C2×C4×Dic719, C2×(C2×D719)⋊C4, … |
| maximal normal subgroup of | C719⋊#95, C2×C4×Dic719, C2×(C2×D719)⋊C4, … |
| maximal quotient of | C2×C4×Dic719, C2×C22⋊Dic719, C2×C4⋊Dic719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11504, 33);