Finite Group DatabasebetaFinite Group Databasebeta| order | 904 |
| isoclinism | isoclinic class of #11744762 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C113 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C113 | C8 |
| prime radical | D113 | C4 |
| cosocle | #90673 | C2 |
| LCS | G ▷ C113 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 113 |
Polycyclic presentation:
2^3,113|a^2=b,b^2=c,d^a=d^44,d^b=d^15,d^c=d^11222 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11744762, #14268661, #72210637 |
| maximal normal subgroup of | C2×#11744762, #14268661, #72210637 |
| maximal quotient of | #14268659, C2×#11744762 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(904, 12);