Finite Group Databasebeta

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C4×#66244 #13046141

order1280
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×#66244

Splittings

FittingC4×2−1+4 ⋊ D5
derived2−1+4⋊C5 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4(C24⋊C5)⋊C2
commutator, hypocenter2−1+4⋊C5C2×C4
Frattini, socleC22C2×(C24⋊C5)⋊C2
FittingC4×2−1+4D5
prime radicalC2×#66244C2
cosocleC2×2−1+4⋊C5C22
LCSG ▷ 2−1+4⋊C5
UCSC1 ◁ C2×C4

436 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 128

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116409);