Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #10597167 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C52 ⋊ C3⋊C8 |
| derived, Hall | C52⋊C3 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C3 | C8 |
| Fitting, socle | C52 | C3⋊C8 |
| prime radical | (C5⋊D5)⋊C3 | C4 |
| cosocle | #1043⋊C3 | C2 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 | |
19 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25 |
Polycyclic presentation:
2^3,3,5^2|a^2=b,b^2=c,d^a=d^2,e^a=e^2f^4,f^a=e^2f^3,e^b=e^2,f^b=f^2,e^c=e^4,f^c=f^4,e^d=f,f^d=e^4f^413 conjugacy classes — view the full character table.
| maximal subgroup of | AΓL(1,𝔽25), C2×#10597167, C3×#10597167, … |
| maximal normal subgroup of | AΓL(1,𝔽25), C2×#10597167, C3×#10597167 |
| maximal quotient of | #11925275, C2×#10597167, #14268076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 148);