Finite Group DatabasebetaFinite Group Databasebeta| order | 23008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C719 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D719 |
| commutator, socle | C2×C719 | C22×C4 |
| Fitting, prime radical | #41×C719 | C2 |
| cosocle | C4×C719 | C23 |
| hypercenter | #41 | D719 |
| hypocenter | C719 | #131 |
| LCS | G ▷ C2×C719 ▷ C719 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11504 |
Polycyclic presentation:
2^5,719|a^2=d,d^2=e,f^a=f^718,c^b=ce3610 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23008, 153);