Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20301501 |
| Fitting | C22×C4×C461 ⋊ C2 |
| Sylow | C461 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D461 |
| commutator, cosocle | C2×C461 | C24 |
| Frattini | C2 | C23×D461 |
| Fitting | C22×C4×C461 | C2 |
| socle | C22×C461 | C23 |
| hypercenter | C22×C4 | D461 |
| hypocenter | C461 | C2×#41 |
| LCS | G ▷ C2×C461 ▷ C461 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7376 |
3700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44442041, #44442042, #44442044, … |
| maximal normal subgroup of | #44442041, #44442042, #44442044, … |
| maximal quotient of | C2×#28414075, C2×#28414077, C2×C4×C22⋊D461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 189);