Finite Group DatabasebetaFinite Group Databasebeta| order | 11504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D719 |
| Fitting | Q8×C719 ⋊ C2 |
| Sylow | C719 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D719 |
| commutator, socle, cosocle | C2×C719 | C23 |
| Fitting | Q8×C719 | C2 |
| prime radical | C2×D719 | C22 |
| hypercenter | Q8 | D719 |
| hypocenter | C719 | C2×Q8 |
| LCS | G ▷ C2×C719 ▷ C719 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
1805 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D719, Q16×D719, #37527623, … |
| maximal normal subgroup of | SD16×D719, Q16×D719, #37527623, … |
| maximal quotient of | C4⋊C4×D719, #37527559, Q8×Dic719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11504, 37);