Finite Group Databasebeta

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C2×#72220732 #72242394

order6400
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#72220732

Splittings

FittingC2×C4×C52×D4 ⋊ C4
SylowC52 ⋊ C2×#1762

Subgroups

subgroupG/H
centerC23C2×C22⋊#1043
commutatorC4×C52C22×C42
FrattiniC2×C4C23×#1043
FittingC2×C4×C52×D4C4
socleC23×C52C2×C22⋊C4
prime radicalC22×D4×C5⋊D5C22
cosocleC2×C4×C5⋊D5C24
hypercenterC2×C4×D4#1043
hypocenterC52C2×#1762
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

8472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1600

Conjugacy classes & character table

328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#442×#1043
maximal normal subgroup ofC2×#442×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.