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C4×D4⋊#1057 #16780449

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×D4⋊#1057

Splittings

SylowC13 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC22×C4C22⋊#261
commutatorC4×C13C2×C4×C8
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13C4×D4⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087098);