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C4⋊C4×#676 #12097288

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4⋊C4×#676

Splittings

FittingC5×C8×C4⋊C4 ⋊ C2
SylowC5 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D5
commutatorC22×C5C22×C42
FittingC5×C8×C4⋊C4C2
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenterC8×C4⋊C4D5
hypocenterC5C4⋊C4×M16
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 167556);