Finite Group Databasebeta

C22×Dic206 #15693061

order3296
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic206

Splittings

SylowC103 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D103
commutator, cosocleC2×C103C24
FrattiniC2C23×D103
FittingC22×C4×C103C2
socle, prime radicalC23×C103C22
hypercenterC22×C4D103
hypocenterC103C22×Q8
LCSG ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3296

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3296, 186);