Finite Group DatabasebetaFinite Group Databasebeta| order | 23008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C719 ⋊ C2 |
| Sylow | C719 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D719 |
| commutator, socle, cosocle | C22×C719 | C23 |
| Fitting | C22⋊C4×C719 | C2 |
| hypercenter | C22⋊C4 | D719 |
| hypocenter | C719 | #120 |
| LCS | G ▷ C22×C719 ▷ C719 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5752 |
Polycyclic presentation:
2^5,719|b^a=bd,c^a=ce,f^a=f^718,f^c=f^7183604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23008, 116);