Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1039 |
| Sylow | C52 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C73 | C4 |
| LCS | G ▷ C52×C73 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,73|a^2=b,c^a=c^4,d^a=d^4,e^a=e^27,e^b=e^72478 conjugacy classes — view the full character table.
| maximal subgroup of | #36346464, #36346466, #36346490, … |
| maximal normal subgroup of | #36346464, #36346466, #36346490, … |
| maximal quotient of | C3×#20300502, C3⋊#20300502 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 41);