Finite Group Databasebeta

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C2×C3⋊D3×#11717375 #72260484

order28800
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C3

Aliases

direct productC2×C3⋊D3×#11717375

Splittings

FittingC23×C32×C52 ⋊ C22×C4
HallC32×C52 ⋊ C22×C4×D4
SylowC52 ⋊ C2×C4×D4×C3⋊D3
SylowC32 ⋊ C22×#11717375

Subgroups

subgroupG/H
centerC22C2×C3⋊D3×D5⋊AGL(1,𝔽5)
commutatorC2×C32×C52C24×C4
FrattiniC2C22×C3⋊D3×D5⋊AGL(1,𝔽5)
FittingC23×C32×C52C22×C4
socleC22×C32×C52C23×C4
prime radicalC2×C3⋊D3×#87886C2
cosocleC2×C32×C5⋊D5C25
hypercenterC23C3⋊D3×D5⋊AGL(1,𝔽5)
hypocenterC32×C52C22×C4×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C22 ◁ C23

38508 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.