Finite Group Databasebeta

Q8×C23⋊C16 #15675301

order2944
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productQ8×C23⋊C16

Splittings

SylowC23 ⋊ Q8×C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×D23
commutatorC2×C23C22×C16
FittingC8×Q8×C23C2
socle, prime radicalC22×C23C22×C8
cosocleC2×C8×C23C23
hypercenterC8×Q8D23
hypocenterC23Q8×C16
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C8 ◁ C8×Q8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6414);