Finite Group Databasebeta

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D4×(C22⋊D83)⋊C4 #35564186

order21248
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×(C22⋊D83)⋊C4

Splittings

FittingD4×C22⋊C4×C83 ⋊ C2
SylowC83 ⋊ C4×D42

Subgroups

subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingD4×C22⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC2×D4×C22⋊D83C2
hypercenterD4×C22⋊C4D83
hypocenterC83C4×D42
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ D4×C22⋊C4

4804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 329350);