Finite Group Databasebeta

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C2×#13104807 #72253222

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13104807

Splittings

FittingC2×C52×#41 ⋊ C4
SylowC52 ⋊ C2×#416

Subgroups

subgroupG/H
centerC2×C4C22⋊#1043
commutatorC4×C52C23×C4
FrattiniC4C23×#1043
FittingC2×C52×#41C4
socleC22×C52C2×C22⋊C4
prime radicalC2×#41×C5⋊D5C2
cosocleC4×C5⋊D5C24
hypercenterC2×#41#1043
hypocenterC52C2×#416
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

3168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#135×#1043, C2×#72253176, C2×#72253172
maximal normal subgroup ofC2×#135×#1043, C2×#72253176, C2×#72253172

GAP

Past the SmallGroups library coverage — no SmallGroups id.