Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C25×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1035 |
| Sylow | C25 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C73 | C4 |
| Frattini | C5 | #13091733 |
| socle | C5×C73 | AGL(1,𝔽5) |
| LCS | G ▷ C25×C73 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,73,5|a^2=b,c^5=e^2,c^a=c^3e,d^a=d^27,e^a=e^3,c^b=c^4e^3,d^b=d^72,e^b=e^4460 conjugacy classes — view the full character table.
| maximal subgroup of | #20300470⋊C3, C3×#20300470, C3⋊#20300470 |
| maximal normal subgroup of | #20300470⋊C3, C3×#20300470 |
| maximal quotient of | C3×#20300470, C3⋊#20300470 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 9);