Finite Group Databasebeta

← Prev (#36339327) Next (#36339329) →

C3×C5×C7×Dic51 #36339328

order21420
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×Dic51
unambiguous semidirect productC3⋊(C3×C5×C7×Dic17)

Splittings

derivedC3×C17 ⋊ C3×C4×C5×C7
HallC32×C5×C7×C17 ⋊ C4
HallC32×C7×C17 ⋊ C4×C5
HallC32×C5×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C3×Dic3
HallC32×C5×C7 ⋊ Dic17
HallC32×C17 ⋊ C4×C5×C7
HallC7×C17 ⋊ C3×C5×Dic3
HallC5×C17 ⋊ C3×C7×Dic3
HallC32×C7 ⋊ C5×Dic17
HallC32×C5 ⋊ C7×Dic17
SylowC17 ⋊ C3×C5×C7×Dic3
SylowC32 ⋊ C5×C7×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D51
commutator, hypocenterC3×C17C3×C4×C5×C7
FrattiniC2C3×C5×C7×D51
Fitting, socle, prime radicalC2×C32×C5×C7×C17C2
cosocleC2×C3×C17C2×C3×C5×C7
LCSG ▷ C3×C17
UCSC1 ◁ C2×C3×C5×C7

112 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7140

Conjugacy classes & character table

5670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 160);