Finite Group Databasebeta

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C2×#13104057 #72242523

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13104057

Splittings

FittingC2×C52×D4 ⋊ C2×C4
SylowC52 ⋊ C2×C4×D8

Subgroups

subgroupG/H
centerC22#11717377
commutatorC4×C52C23×C4
FrattiniC4C22×D5⋊AGL(1,𝔽5)
FittingC2×C52×D4C2×C4
socleC22×C52C4×D4
prime radicalC2×#11717044C2
cosocleC4×C5⋊D5C24
hypercenterC2×D4D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×D8
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D8×D5⋊AGL(1,𝔽5), #72253344, #72253350
maximal normal subgroup ofC2×D8×D5⋊AGL(1,𝔽5), #72253344, #72253350

GAP

Past the SmallGroups library coverage — no SmallGroups id.