Finite Group Databasebeta

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C2×#13104048 #72221369

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13104048

Splittings

FittingC22×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C2×#385

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC22×C52C23×C4
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC23×D52C22
cosocleC22×C5⋊D5C24
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×#385
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

2882 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213578
maximal normal subgroup ofC2×#72213578
maximal quotient ofC2×#72213383, #72226373, #72226524, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.