Finite Group DatabasebetaFinite Group Databasebeta| order | 23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C373 ⋊ C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D373 |
| commutator | C2×C373 | C2×C42 |
| Fitting | #95×C373 | C2 |
| socle, prime radical, cosocle | C23×C373 | C23 |
| hypercenter | #95 | D373 |
| hypocenter | C373 | C4×C4⋊C4 |
| LCS | G ▷ C2×C373 ▷ C373 | |
| UCS | C1 ◁ C23 ◁ #95 | |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23872 |
Polycyclic presentation:
2^6,373|a^2=e,b^2=f,c^2=de,b^a=bd,g^c=g^3723760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23872, 400);