Finite Group DatabasebetaFinite Group Databasebeta| order | 1928 |
| isoclinism | isoclinic class of #14515358 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C241 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C241 | C8 |
| prime radical | D241 | C4 |
| cosocle | #11757210 | C2 |
| LCS | G ▷ C241 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 241 |
| transitive degree | μt(G) = 241 |
Polycyclic presentation:
2^3,241|a^2=b,b^2=c,d^a=d^30,d^b=d^177,d^c=d^24038 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14515358, #16838784, #72222897, … |
| maximal normal subgroup of | C2×#14515358, #16838784, #72222897, … |
| maximal quotient of | #16838782, C2×#14515358 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1928, 15);