Finite Group Databasebeta

C22×Dic274 #17984128

order4384
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic274

Splittings

SylowC137 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D137
commutator, cosocleC2×C137C24
FrattiniC2C23×D137
FittingC22×C4×C137C2
socle, prime radicalC23×C137C22
hypercenterC22×C4D137
hypocenterC137C22×Q8
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4384

Conjugacy classes & character table

1108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4384, 186);