Finite Group DatabasebetaFinite Group Databasebeta| order | 12054 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C2×C41×#3861 |
| Fitting, socle, Hall | C2×C72×C41 ⋊ C3 |
| derived, Sylow | C72 ⋊ C2×C3×C41 |
| Hall | C72×C41 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | #3861 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C41 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C41 | |
80 conjugacy classes of subgroups.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#10596874, #37563039, C41×#10596873, … |
| maximal normal subgroup of | C41×#10596874, #37563039, C41×#10596873, … |
| maximal quotient of | C4×C41×#3861, C22×C41×#3861, C2×C41×#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12054, 35);