Finite Group Databasebeta

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C4×#11717363 #72220808

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11717363

Splittings

FittingC42×C52 ⋊ C2×C4
SylowC52 ⋊ C42×D4

Subgroups

subgroupG/H
centerC2×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C42
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC42×C52C2×C4
socleC22×C52C23×C4
prime radicalC2×#87877C22
cosocleC22×C5⋊D5C24
hypercenterC42D5⋊AGL(1,𝔽5)
hypocenterC52C42×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C42

2106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72220815, C2×C4×#11717363, #72226403, …
maximal normal subgroup of#72220815, C2×C4×#11717363, #72226403, …
maximal quotient of#72220809, #72223022, #72223043, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.