Finite Group Databasebeta

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C2×C3⋊D2415 #44394684

order28980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D2415
unambiguous semidirect product(C2×C3)⋊D2415
unambiguous semidirect product(C2×C5)⋊(C3⋊D483)
unambiguous semidirect product(C2×C7)⋊(C3⋊D345)
unambiguous semidirect product(C2×C23)⋊(C3⋊D105)

Splittings

Fitting, socleC2×C32×C5×C7×C23 ⋊ C2
derived, HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C2×D5
HallC32×C5×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D23
HallC32×C23 ⋊ C2×D35
HallC7×C23 ⋊ C2×C3⋊D15
HallC5×C23 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×D115
HallC32×C5 ⋊ C2×D161
HallC5×C7 ⋊ C2×C3⋊D69
SylowC23 ⋊ C2×C3⋊D105
SylowC32 ⋊ C2×D805
SylowC7 ⋊ C2×C3⋊D345
SylowC5 ⋊ C2×C3⋊D483

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D2415
commutator, cosocle, hypocenterC32×C5×C7×C23C22
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C23C2
LCSG ▷ C32×C5×C7×C23
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14490

Conjugacy classes & character table

7248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 353);