Finite Group Databasebeta

Q16×C4⋊Dic83 #35422836

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ16×C4⋊Dic83

Splittings

SylowC83 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×C4×Q16×C83C2
socle, prime radicalC23×C83C22×D4
cosocleC22×C4×C83C24
hypercenterC2×C4×Q16D83
hypocenterC83C4⋊C4×Q16
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 188000);