Finite Group DatabasebetaFinite Group Databasebeta| order | 11824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic739⋊C4 |
| Sylow | C739 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D739 |
| commutator | C2×C739 | C2×C4 |
| Fitting | C2×C4×C739 | C2 |
| socle, prime radical, cosocle | C22×C739 | C22 |
| hypercenter | C2×C4 | D739 |
| hypocenter | C739 | C4⋊C4 |
| LCS | G ▷ C2×C739 ▷ C739 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,739|a^2=d,b^2=c,b^a=bc,e^b=e^7382962 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C4×D739, C2×Dic739⋊C4, #37556616, … |
| maximal normal subgroup of | C4⋊C4×D739, C2×Dic739⋊C4, #37556616, … |
| maximal quotient of | C739⋊#95, Dic739⋊C8, #37556591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11824, 19);