Finite Group Databasebeta

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C22×#11717363 #72223016

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11717363

Splittings

FittingC22×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C24×C4
FrattiniC2C23×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC22×#87877C2
cosocleC2×C5⋊D5C25
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C22×C4×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

5554 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×#11717363, C22×D4×D5⋊AGL(1,𝔽5)
maximal normal subgroup ofC2×C4×#11717363, C22×D4×D5⋊AGL(1,𝔽5)
maximal quotient of#72223017, #72223074, C2×C4×#11717363, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.