Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C337 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D337 |
| commutator | C2×C337 | C42 |
| Fitting | C22×C4×C337 | C2 |
| socle, prime radical, cosocle | C23×C337 | C22 |
| hypercenter | C22×C4 | D337 |
| hypocenter | C337 | #95 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=e,b^a=bc,f^b=f^3362708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341039, #36341040, #36341042, … |
| maximal normal subgroup of | #36341039, #36341040, #36341042, … |
| maximal quotient of | #36341059, #36341060, #36341061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 53);