Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C457 ⋊ C2 |
| Sylow | C457 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D457 |
| commutator, socle, cosocle | C22×C457 | C23 |
| Fitting | C22⋊C4×C457 | C2 |
| hypercenter | C22⋊C4 | D457 |
| hypocenter | C457 | #120 |
| LCS | G ▷ C22×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3656 |
Polycyclic presentation:
2^5,457|b^a=bd,c^a=ce,f^a=f^456,f^c=f^4562294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416965, #120×D457, C2×#28410522, … |
| maximal normal subgroup of | #44416965, #120×D457, C2×#28410522, … |
| maximal quotient of | #44416632, #44416651, #44416652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 116);