Finite Group Databasebeta

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C2×#72253147 #72253244

order6400
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#72253147

Splittings

FittingC2×C52×#135 ⋊ C4
SylowC52 ⋊ C22×#444

Subgroups

subgroupG/H
centerC2×C4D4×#1043
commutatorC4×C52C24×C4
FrattiniC4C24×#1043
FittingC2×C52×#135C4
socleC22×C52C2×C4×D4
prime radicalC2×#135×C5⋊D5C2
cosocleC4×C5⋊D5C25
hypercenterC2×#135#1043
hypocenterC52C22×#444
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

10840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#444×#1043
maximal normal subgroup ofC2×#444×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.