Finite Group Databasebeta

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C2×#13104045 #72221160

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13104045

Splittings

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

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C42
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC23×D52C22
cosocleC22×C5⋊D5C24
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

3218 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, C2×#72221487, C2×#72213578
maximal normal subgroup ofC2×C4×#11717363, C2×#72221487, C2×#72213578
maximal quotient ofC2×#72213321, #72223101, #72226525, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.