Finite Group Databasebeta

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C2×C3×D15×C31 #19150181

order5580
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C22×C3×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D15×C31
unambiguous semidirect product(C2×C3)⋊(C3×D5×C31)
unambiguous semidirect product(C2×C5)⋊(C3×D3×C31)

Splittings

Fitting, socleC2×C32×C5×C31 ⋊ C2
derivedC3×C5 ⋊ C22×C3×C31
HallC32×C5×C31 ⋊ C22
HallC32×C31 ⋊ C2×D5
HallC5×C31 ⋊ C2×C3×D3
HallC32×C5 ⋊ C22×C31
SylowC32 ⋊ C2×D5×C31
SylowC5 ⋊ C2×C3×D3×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31D15
commutator, hypocenterC3×C5C22×C3×C31
FrattiniC1G
Fitting, socleC2×C32×C5×C31C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C31

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1674 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C31×D75, C2×C3×D15×ΓL(1,𝔽32), C3×D5×D15×C31, …
maximal normal subgroup ofC2×C3×D15×ΓL(1,𝔽32), C2×C3×C5×D15×C31
maximal quotient ofC2×C3×C31×D75, C3×D5×D15×C31, C2×C3×C5×D15×C31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 170);