Finite Group Databasebeta

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C2×#13107559 #72220771

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13107559

Splittings

FittingC22×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC2×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C24×C4
FrattiniC2C23×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC22×C52C23×C4
prime radicalC2×#11717471C2
cosocleC2×C5⋊D5C25
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4

3954 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213412, C2×#72213321, #72221166, …
maximal normal subgroup ofC2×#72213412, C2×#72213321, #72221166, …
maximal quotient ofC2×C4×#11717363, #72226493, #72226604, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.