Finite Group Databasebeta

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C5×#10602143 #72223131

order3200
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#10602143

Splittings

FittingC52×#498 ⋊ C2
SylowC52 ⋊ #2230

Subgroups

subgroupG/H
centerC2×C5#65373
commutator, cosocleC2×C5×C8C23×C5
FrattiniC2×C8C22×C5×D5
FittingC52×#498C2
socleC2×C52#476
prime radicalC5×#4050C22
hypercenterC5×#498D5
hypocenterC5C5×#2230
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ C5×#498

350 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223136
maximal normal subgroup of#72223136

GAP

Past the SmallGroups library coverage — no SmallGroups id.