Finite Group Databasebeta

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C2×#13103057 #72253232

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5

Aliases

direct productC2×#13103057

Splittings

SylowC52 ⋊ C2×#444

Subgroups

subgroupG/H
centerC2×C4D4×C5⋊D5
commutatorC4×C52C23×C4
FrattiniC2×C4C23×C5⋊D5
Fitting, prime radicalC2×C52×#135C2
socleC22×C52C4×D4
cosocleC2×C4×C52C24
hypercenterC2×#135C5⋊D5
hypocenterC52C2×#444
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C5⋊D5×#444
maximal normal subgroup ofC2×C5⋊D5×#444

GAP

Past the SmallGroups library coverage — no SmallGroups id.