Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C52⋊C3 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ Dic3⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | #3874⋊C2 |
| commutator | C2×C52⋊C3 | C2×C4 |
| Fitting, socle | C22×C52 | C2×D3 |
| prime radical, cosocle | C22×C52⋊C3 | C22 |
| hypocenter | C52⋊C3 | C4⋊C4 |
| LCS | G ▷ C2×C52⋊C3 ▷ C52⋊C3 | |
| UCS | C1 ◁ C22 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=c,b^a=bd,e^a=e^2,f^a=g,g^a=f,e^b=e^2,f^b=g^4,g^b=f^4,f^e=g,g^e=f^4g^450 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 224);