Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C337 ⋊ C2 |
| Sylow | C337 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D337 |
| commutator, socle | C2×C337 | C22×C4 |
| Fitting | M16×C337 | C2 |
| prime radical | #19129185 | C2 |
| cosocle | C4×C337 | C23 |
| hypercenter | M16 | D337 |
| hypocenter | C337 | #131 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,d^2=e,f^a=f^336,c^b=ce,f^c=f^3361700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341419, #36341421, #36341424, … |
| maximal normal subgroup of | #36341419, #36341421, #36341424, … |
| maximal quotient of | #36341262, #36341263, #36341270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 154);