Finite Group Databasebeta

C22⋊Q8×#90673 #28407040

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×#90673

Splittings

FittingC22⋊Q8×C113 ⋊ C4
SylowC113 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
FittingC22⋊Q8×C113C4
prime radicalC23×D113C23
cosocleC22×D113C24
hypercenterC22⋊Q8#90673
hypocenterC113C4×C22⋊Q8
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20976);