Finite Group Databasebeta

C22×Q8×D52 #16769836

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×Q8×D52

Splittings

FittingC22×C4×Q8×C13 ⋊ C2
SylowC13 ⋊ C22×D4×Q8

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C4×Q8×C13C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC22×C4×Q8D13
hypocenterC13C22×D4×Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

11798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076485);