Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C241 ⋊ C2 |
| Sylow | C241 ⋊ #534 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D241 |
| commutator, socle, cosocle | C22×C241 | C24 |
| Fitting | C2×C22⋊C4×C241 | C2 |
| hypercenter | C2×C22⋊C4 | D241 |
| hypocenter | C241 | #534 |
| LCS | G ▷ C22×C241 ▷ C241 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|b^a=be,c^a=cf,d^a=de,g^a=g^240,c^b=ce,g^c=g^2402422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506362, #44506365, #44506396, … |
| maximal normal subgroup of | #44506362, #44506365, #44506396, … |
| maximal quotient of | #44510020, #44510059, #44510105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1111);