Finite Group Databasebeta

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C2×C5⋊D5×#3811 #72259800

order14400
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210×C5

Aliases

direct productC2×C5⋊D5×#3811

Splittings

FittingC23×C32×C52 ⋊ C23
HallC32×C52 ⋊ C23×D4
SylowC52 ⋊ C22×#3811
SylowC32 ⋊ C22×D4×C5⋊D5

Subgroups

subgroupG/H
centerC22C2×D32×C5⋊D5
commutator, cosocleC2×C32×C52C25
FrattiniC2C22×D32×C5⋊D5
FittingC23×C32×C52C23
socleC22×C32×C52C24
hypercenterC23D32×C5⋊D5
hypocenterC32×C52C23×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C22 ◁ C23

24784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#1043×#3811
maximal normal subgroup ofC2×#1043×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.