Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| isoclinism | isoclinic class of #64516 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D152 |
| Fitting | C2×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D76 |
| commutator, cosocle | C4×C19 | C23 |
| Frattini | C4 | C22×D19 |
| Fitting | C2×C8×C19 | C2 |
| socle | C22×C19 | D4 |
| hypercenter | C2×C8 | D19 |
| hypocenter | C19 | C2×D8 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
158 conjugacy classes — view the full character table.
| maximal subgroup of | #11926344, #11926346, #11926356, … |
| maximal normal subgroup of | #11926344, #11926346, #11926356, … |
| maximal quotient of | C2×#10597278, C2×#10597275, C4×D152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 98);