Finite Group Databasebeta

C22×Dic272 #17192447

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic272

Splittings

SylowC17 ⋊ C22×Q64

Subgroups

subgroupG/H
centerC23D272
commutator, cosocleC16×C17C24
FrattiniC16C23×D17
FittingC22×C17×C32C2
socle, prime radicalC23×C17D16
hypercenterC22×C32D17
hypocenterC17C22×Q64
LCSG ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×C32

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327691);