Finite Group Databasebeta

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C2×#13046134 #72209696

order2560
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13046134

Splittings

derived2−1+4⋊C5 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22×C4(C24⋊C5)⋊C2
commutator, hypocenter2−1+4⋊C5C22×C4
FrattiniC22C22×(C24⋊C5)⋊C2
FittingC22×#585D5
socleC23C2×(C24⋊C5)⋊C2
prime radicalC22×#585⋊C5C2
cosocleC2×2−1+4⋊C5C23
LCSG ▷ 2−1+4⋊C5
UCSC1 ◁ C22×C4

5407 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 5407 conjugacy classes of subgroups — too many to draw. Only its 70 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

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72209698
maximal quotient of#72209978

GAP

Past the SmallGroups library coverage — no SmallGroups id.