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C2×C3⋊D255 #15690397

order3060
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D255
unambiguous semidirect product(C2×C3)⋊D255
unambiguous semidirect product(C2×C5)⋊(C3⋊D51)
unambiguous semidirect product(C2×C17)⋊(C3⋊D15)

Splittings

Fitting, socleC2×C32×C5×C17 ⋊ C2
derived, HallC32×C5×C17 ⋊ C22
HallC32×C17 ⋊ C2×D5
HallC5×C17 ⋊ C2×C3⋊D3
HallC32×C5 ⋊ C2×D17
SylowC17 ⋊ C2×C3⋊D15
SylowC32 ⋊ C2×D85
SylowC5 ⋊ C2×C3⋊D51

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D255
commutator, cosocle, hypocenterC32×C5×C17C22
FrattiniC1G
Fitting, socleC2×C32×C5×C17C2
LCSG ▷ C32×C5×C17
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1530

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D1275, D5×C3⋊D255, C2×C3⋊(C3⋊(C5⋊D85)), …
maximal normal subgroup ofC2×C5×C3⋊D255, C2×C7×C3⋊D255, C2×C11×C3⋊D255
maximal quotient ofC2×C3⋊D1275, D5×C3⋊D255, C2×C3⋊(C3⋊(C5⋊D85)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3060, 102);