Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C19 ⋊ #2582 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator, socle, prime radical, cosocle | C23×C19 | C24 |
| Fitting | C2×C4×Q8×C19 | C2 |
| hypercenter | C2×C4×Q8 | D19 |
| hypocenter | C19 | #2582 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^7,19|a^2=e,b^2=eg,c^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^18398 conjugacy classes — view the full character table.
| maximal subgroup of | #18084846, #18084849, #18084872, … |
| maximal normal subgroup of | #18084846, #18084849, #18084872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 9880);