Finite Group DatabasebetaFinite Group Databasebeta| order | 4508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D23×C7⋊D7 |
| unambiguous semidirect product | (C7×D23)⋊D7 |
| Fitting, socle, derived, Hall | C72×C23 ⋊ C22 |
| Sylow | C72 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C23 | C22 |
| LCS | G ▷ C72×C23 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1127 |
338 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×#64424, D23×#64425, D23×ΓL(1,𝔽8)⋊D7, … |
| maximal normal subgroup of | D23×#64424, D23×#64425, D23×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | C3×D23×C7⋊D7, D23×C3⋊(C7⋊D7), C7⋊D7×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4508, 18);