Finite Group Databasebeta

C22×Q8×#1055 #16727271

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×#1055

Splittings

SylowC13 ⋊ C22×C8×Q8

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC2×C13C24×C8
FrattiniC2×C4C24×D13
FittingC22×C4×Q8×C13C2
socle, prime radicalC24×C13C22×C4
cosocleC2×C4×C13C25
hypercenterC22×C4×Q8D13
hypocenterC13C22×C8×Q8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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(3328, 1033920);