Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×C41×#3874 |
| Fitting, socle | C2×C52×C41 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C22×C41 |
| Hall | C41×C52⋊C3 ⋊ C22 |
| Hall | C52×C41 ⋊ C2×D3 |
| Sylow | C52 ⋊ C2×D3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C41 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2×C41 | |
60 conjugacy classes of subgroups.
1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C41×#3874, C2×C3×C41×#3874, C2×C41×C3⋊#3874 |
| maximal normal subgroup of | C2×C3×C41×#3874 |
| maximal quotient of | C2×C41×#90646, D3×C41×#3874, C2×C3×C41×#3874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 118);