Finite Group Databasebeta

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C2×#72242325 #72269146

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#72242325

Splittings

FittingC22×C52×D8 ⋊ C4
SylowC52 ⋊ C2×#2140

Subgroups

subgroupG/H
centerC22C2×#11716875
commutatorC52×C8C23×C4
FrattiniC8C23×#1043
FittingC22×C52×D8C4
socleC22×C52C2×#102
prime radicalC22×D8×C5⋊D5C2
cosocleC8×C5⋊D5C24
hypercenterC22×D8#1043
hypocenterC52C2×#2140
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

5624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#509×#1043
maximal normal subgroup ofC2×#509×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.