Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×C22⋊D379 |
| Fitting | C24×C379 ⋊ C2 |
| Sylow | C379 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D379 |
| commutator, cosocle | C2×C379 | C24 |
| Frattini | C2 | C23×D379 |
| Fitting | C24×C379 | C2 |
| socle | C23×C379 | C22 |
| hypercenter | C24 | D379 |
| hypocenter | C379 | C22×D4 |
| LCS | G ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C23 ◁ C24 | |
236 conjugacy classes of subgroups.
3044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37565120, #37565121, #37565123, … |
| maximal normal subgroup of | #37565120, #37565121, #37565123, … |
| maximal quotient of | C22×(C2×D379)⋊C4, C22×C22⋊Dic379, C22×Dic379⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 183);