Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C577 ⋊ C2 |
| Sylow | C577 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D577 |
| commutator, socle, cosocle | C22×C577 | C23 |
| Fitting | C4⋊C4×C577 | C2 |
| prime radical | C22×D577 | C22 |
| hypercenter | C4⋊C4 | D577 |
| hypocenter | C577 | #126 |
| LCS | G ▷ C22×C577 ▷ C577 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^5,577|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^576,f^c=f^5762894 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D577, C2×#32914659, #49148476, … |
| maximal normal subgroup of | #126×D577, C2×#32914659, #49148476, … |
| maximal quotient of | #49147816, #49147830, #49147832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 141);