Finite Group Databasebeta

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C2×#13104059 #72221073

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13104059

Splittings

SylowC52 ⋊ C2×C4×SD16

Subgroups

subgroupG/H
centerC22#11717375
commutatorC4×C52C23×C4
FrattiniC4C22×D5⋊AGL(1,𝔽5)
FittingC2×C52×D4C2×C4
socleC22×C52C4×D4
prime radicalC2×D4×C5⋊D5C22
cosocleC4×C5⋊D5C24
hypercenterC2×D4D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×SD16
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

1530 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213282, #72221374, #72223366, …
maximal normal subgroup ofC2×#72213282, #72221374, #72223366, …
maximal quotient of#72226594, D3×#13104059, #72242644

GAP

Past the SmallGroups library coverage — no SmallGroups id.