Finite Group Databasebeta

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C3×C5×C3⋊(C7⋊#595) #36339454

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

Aliases

direct productC3×C5×C3⋊(C7⋊#595)
unambiguous semidirect productC3⋊(C3×C5×C7⋊#595)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derivedC3×C7×C17 ⋊ C3×C4×C5
HallC32×C7×C17 ⋊ C4×C5
HallC32×C5×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ C3×Dic3
HallC32×C5×C7 ⋊ #595
HallC32×C17 ⋊ C5×Dic7
HallC7×C17 ⋊ C3×C5×Dic3
HallC5×C17 ⋊ C3×Dic21
HallC32×C7 ⋊ C5×#595
HallC32×C5 ⋊ C7⋊#595
HallC5×C7 ⋊ C3×C3⋊#595
SylowC17 ⋊ C3×C5×Dic21
SylowC32 ⋊ C5×C7⋊#595
SylowC7 ⋊ C3×C5×C3⋊#595

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊(C7⋊#595)
commutator, hypocenterC3×C7×C17C3×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC32×C5×C7×D17C2
cosocleC3×C7×D17C2×C3×C5
LCSG ▷ C3×C7×C17
UCSC1 ◁ C3×C5

112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 3570

Conjugacy classes & character table

1620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 286);