Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C379 ⋊ C2 |
| Sylow | C379 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D379 |
| commutator, socle | C2×C379 | C22×C4 |
| Fitting | M16×C379 | C2 |
| prime radical | #20258606 | C2 |
| cosocle | C4×C379 | C23 |
| hypercenter | M16 | D379 |
| hypocenter | C379 | #131 |
| LCS | G ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,379|a^2=d,d^2=e,f^a=f^378,c^b=ce,f^c=f^3781910 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37565358, #37565360, #37565363, … |
| maximal normal subgroup of | #37565358, #37565360, #37565363, … |
| maximal quotient of | #37565201, #37565202, #37565209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 154);