Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C241 ⋊ C2 |
| Sylow | C241 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D241 |
| commutator, socle | C2×C241 | C22×C8 |
| Fitting | M32×C241 | C2 |
| prime radical | #16838770 | C4 |
| cosocle | C8×C241 | C23 |
| hypercenter | M32 | D241 |
| hypocenter | C241 | #504 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=d,d^2=e,e^2=f,g^a=g^240,c^b=cf,g^c=g^2402440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44509279, #44509281, #44509284, … |
| maximal normal subgroup of | #44509279, #44509281, #44509284, … |
| maximal quotient of | #44509043, #44509044, #44509057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 967);