Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52⋊C3 ⋊ C8 |
| Sylow | C52 ⋊ C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #64480 |
| commutator, hypocenter | C52⋊C3 | C8 |
| Fitting, socle | C2×C52 | Dic3 |
| prime radical | C2×C52⋊C3 | C4 |
| cosocle | #1039⋊C3 | C2 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5^2|a^2=b,b^2=c,d^a=d^2,e^a=e^3f^3,f^a=f^2,e^b=e^4,f^b=f^4,e^d=ef,f^d=e^2f^316 conjugacy classes — view the full character table.
| maximal subgroup of | #11925277, #11925278, #11925282, … |
| maximal normal subgroup of | #11925277, #11925278, #11925282, … |
| maximal quotient of | #11925000, C2×#10597074, #14267932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 55);