Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20300742 |
| Fitting | C2×Q8×C457 ⋊ C2 |
| Sylow | C457 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D457 |
| commutator, cosocle | C2×C457 | C24 |
| Frattini | C2 | C23×D457 |
| Fitting | C2×Q8×C457 | C2 |
| socle | C22×C457 | C23 |
| hypercenter | C2×Q8 | D457 |
| hypocenter | C457 | C2×#41 |
| LCS | G ▷ C2×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
2300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416760, #44416772, #44416777, … |
| maximal normal subgroup of | #44416760, #44416772, #44416777, … |
| maximal quotient of | C2×#28410510, C2×#28410514, C2×Q8×Dic457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 190);