Finite Group Databasebeta

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C2×C3×C29×D15 #19104897

order5220
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C29×D15
unambiguous semidirect product(C2×C3)⋊(C3×D5×C29)
unambiguous semidirect product(C2×C5)⋊(C3×D3×C29)

Splittings

Fitting, socleC2×C32×C5×C29 ⋊ C2
derivedC3×C5 ⋊ C22×C3×C29
HallC32×C5×C29 ⋊ C22
HallC32×C29 ⋊ C2×D5
HallC5×C29 ⋊ C2×C3×D3
HallC32×C5 ⋊ C22×C29
SylowC32 ⋊ C2×D5×C29
SylowC5 ⋊ C2×C3×D3×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D15
commutator, hypocenterC3×C5C22×C3×C29
FrattiniC1G
Fitting, socleC2×C32×C5×C29C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C29

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1566 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C29×D75, C3×D5×C29×D15, C2×C3×C5×C29×D15, …
maximal normal subgroup ofC2×C3×C5×C29×D15, C2×C3×D15×C29⋊C7, C2×C3×C7×C29×D15
maximal quotient ofC2×C3×C29×D75, C3×D5×C29×D15, C2×C3×C5×C29×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5220, 107);