Finite Group Databasebeta

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C3×Dic1785 #36339322

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

Aliases

direct productC3×Dic1785
unambiguous semidirect productC3⋊(C3×Dic595)

Splittings

derivedC3×C5×C7×C17 ⋊ C3×C4
HallC32×C5×C7×C17 ⋊ C4
HallC32×C7×C17 ⋊ Dic5
HallC32×C5×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ C3×Dic3
HallC32×C5×C7 ⋊ Dic17
HallC32×C17 ⋊ Dic35
HallC7×C17 ⋊ C3×Dic15
HallC5×C17 ⋊ C3×Dic21
HallC32×C7 ⋊ Dic85
HallC32×C5 ⋊ Dic119
HallC5×C7 ⋊ C3×Dic51
SylowC17 ⋊ C3×Dic105
SylowC32 ⋊ Dic595
SylowC7 ⋊ C3×Dic255
SylowC5 ⋊ C3×Dic357

Subgroups

subgroupG/H
center, hypercenterC2×C3D1785
commutator, hypocenterC3×C5×C7×C17C3×C4
FrattiniC2C3×D1785
Fitting, socle, prime radicalC2×C32×C5×C7×C17C2
cosocleC2×C3×C5×C7×C17C2×C3
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C2×C3

112 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 66 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

5364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 154);