Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C52 ⋊ C2×D3 |
| Hall | C52⋊C3 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×#67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#3874⋊C2 |
| commutator, cosocle | C2×C52⋊C3 | C23 |
| Fitting | C22×C52 | C2×D3 |
| socle | C2×C52 | C22×D3 |
| hypercenter | C22 | #3874⋊C2 |
| hypocenter | C52⋊C3 | C2×D4 |
| LCS | G ▷ C2×C52⋊C3 ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 ◁ C22 | |
162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^4,3,5^2|c^a=cd,e^a=e^2,f^a=fg,g^a=g^4,c^b=cd,e^b=e^2,f^b=f^4g^4,f^e=g,g^e=f^4g^438 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 523);