Finite Group Databasebeta

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C2×C32×#11717375 #72259519

order14400
automorphism?
homologyAbelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×C32×#11717375

Splittings

FittingC23×C32×C52 ⋊ C2×C4
HallC32×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C2×C32×C4×D4

Subgroups

subgroupG/H
centerC22×C32C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C23×C32×C4
FrattiniC2C22×C32×D5⋊AGL(1,𝔽5)
FittingC23×C32×C52C2×C4
socleC22×C32×C52C22×C4
prime radicalC2×C32×#87886C2
cosocleC2×C5⋊D5C24×C32
hypercenterC23×C32D5⋊AGL(1,𝔽5)
hypocenterC52C2×C32×C4×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C32 ◁ C23×C32

6528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D3×#11717375
maximal normal subgroup ofC2×C3⋊D3×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.