Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4×C587 ⋊ C2 |
| Sylow | C587 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D587 |
| commutator, socle, cosocle | C22×C587 | C23 |
| Fitting | C2×D4×C587 | C2 |
| hypercenter | C2×D4 | D587 |
| hypocenter | C587 | #120 |
| LCS | G ▷ C22×C587 ▷ C587 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4696 |
Polycyclic presentation:
2^5,587|b^a=bd,c^a=ce,f^c=f^5862944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49176866, #49176868, #49177267, … |
| maximal normal subgroup of | #49176866, #49176868, #49177267, … |
| maximal quotient of | #49176935, #49176951, #49176952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 114);