Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C727 ⋊ C2 |
| Sylow | C727 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D727 |
| commutator, socle | C2×C727 | C22×C4 |
| Fitting | M16×C727 | C2 |
| prime radical | #26042740 | C2 |
| cosocle | C4×C727 | C23 |
| hypercenter | M16 | D727 |
| hypocenter | C727 | #131 |
| LCS | G ▷ C2×C727 ▷ C727 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
Polycyclic presentation:
2^5,727|a^2=d,d^2=e,f^a=f^726,c^b=ce,f^c=f^7263650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 154);