Finite Group Databasebeta

Q8×#14268622 #28392478

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

Aliases

direct productQ8×#14268622

Splittings

SylowC113 ⋊ Q8×C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×D113
commutatorC2×C113C22×C16
FittingC8×Q8×C113C2
socle, prime radicalC22×C113C22×C8
cosocleC2×C8×C113C23
hypercenterC8×Q8D113
hypocenterC113Q8×C16
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C8 ◁ C8×Q8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6414);