Finite Group Databasebeta

C2×Q16×D467 #44470812

order29888
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q16×D467

Splittings

FittingC2×Q16×C467 ⋊ C2
SylowC467 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC22D4×D467
commutator, cosocleC4×C467C24
FrattiniC4C23×D467
FittingC2×Q16×C467C2
socleC22×C467C2×D4
prime radicalC22×D467D4
hypercenterC2×Q16D467
hypocenterC467C22×Q16
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

3290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1324);