Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4×C727 ⋊ C2 |
| Sylow | C727 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D727 |
| commutator, socle, cosocle | C22×C727 | C23 |
| Fitting | C2×D4×C727 | C2 |
| hypercenter | C2×D4 | D727 |
| hypocenter | C727 | #120 |
| LCS | G ▷ C22×C727 ▷ C727 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5816 |
Polycyclic presentation:
2^5,727|b^a=bd,c^a=ce,f^c=f^7263644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 114);