Finite Group Databasebeta

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C2×C3×C5×C17×D21 #36339580

order21420
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C17×D21
unambiguous semidirect product(C2×C3)⋊(C3×C5×D7×C17)

Splittings

Fitting, socleC2×C32×C5×C7×C17 ⋊ C2
derivedC3×C7 ⋊ C22×C3×C5×C17
HallC32×C5×C7×C17 ⋊ C22
HallC32×C7×C17 ⋊ C22×C5
HallC32×C5×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C22×C17
HallC32×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×C3×C5×D3
HallC32×C7 ⋊ C22×C5×C17
HallC32×C5 ⋊ C2×D7×C17
HallC5×C7 ⋊ C2×C3×D3×C17
SylowC32 ⋊ C2×C5×D7×C17
SylowC7 ⋊ C2×C3×C5×D3×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17D21
commutator, cosocle, hypocenterC3×C7C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C17C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C3×C5×C17

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 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

6120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 412);