Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C52⋊C3 ⋊ Q8 |
| Sylow | C52 ⋊ Dic6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #3874⋊C2 |
| commutator, prime radical, cosocle | C2×C52⋊C3 | C22 |
| Fitting, socle | C2×C52 | C2×D3 |
| hypocenter | C52⋊C3 | Q8 |
| LCS | G ▷ C2×C52⋊C3 ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5^2|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=f^3,f^a=e^2,d^b=d^2,e^b=f^2,f^b=e^3,e^d=e^4f^2,f^d=e^225 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊Q8, #11925299, ((C5⋊D5)⋊C3)⋊Q8, … |
| maximal normal subgroup of | #3874⋊Q8, #11925299, ((C5⋊D5)⋊C3)⋊Q8, … |
| maximal quotient of | #11925014, #11925015, C2×#10597076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 57);