Finite Group Databasebeta

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C2×#13104114 #72223302

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13104114

Splittings

SylowC52 ⋊ C2×#386

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC22×C52C23×C4
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC24×C52C2×C4
socleC23×C52C22×C4
prime radicalC22×#87886C2
cosocleC22×C5⋊D5C24
hypercenterC24D5⋊AGL(1,𝔽5)
hypocenterC52C2×#386
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C24

4514 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal quotient of#72223303, #72223397, #72226416, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.