Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #3874⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#3874⋊C2 |
| unambiguous semidirect product | #3874⋊C22 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊C22 |
| Fitting, socle | C2×C52 ⋊ C2×D3 |
| derived, Hall | C52⋊C3 ⋊ C23 |
| Sylow | C52 ⋊ C22×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #3874⋊C2 |
| commutator, cosocle, hypocenter | C52⋊C3 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | C2×D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
28 conjugacy classes — view the full character table.
| maximal subgroup of | #11925281, C4×#3874⋊C2, #11925303, … |
| maximal normal subgroup of | #11925281, C4×#3874⋊C2, #11925303, … |
| maximal quotient of | #3874⋊Q8, #11925297, #11925298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 154);