Finite Group Databasebeta

Q8×#14268650 #28406987

order14464
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productQ8×#14268650

Splittings

SylowC113 ⋊ Q8×C16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×#90673
commutatorC2×C113C22×C16
FittingC4×Q8×C113C4
socle, prime radicalC22×C113C22×C8
cosocleC2×#11744751C23
hypercenterC4×Q8#90673
hypocenterC113Q8×C16
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C4×Q8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20923);