Finite Group DatabasebetaFinite Group Databasebeta| order | 24444 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊#87604 |
| derived, Hall | C7×C97 ⋊ C4×C9 |
| Hall | C7⋊C9×C97 ⋊ C4 |
| Hall | C7⋊#87604 ⋊ C9 |
| Sylow | C97 ⋊ Dic7⋊C9 |
| Hall | C7⋊C9 ⋊ #87604 |
| Sylow | C7 ⋊ C9×#87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊#87604 |
| commutator, hypocenter | C7×C97 | C4×C9 |
| Fitting, socle | C3×C7×C97 | C3×C4 |
| prime radical, cosocle | C3×C7×D97 | C2×C3 |
| LCS | G ▷ C7×C97 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6111 |
Polycyclic presentation:
2,3,2,7,97,3|a^2=c,b^3=f,d^a=d^6,e^a=e^75,d^b=d^2,e^c=e^96402 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24444, 31);