Finite Group Databasebeta

#455×Dic17 #17040210

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#455×Dic17

Splittings

SylowC17 ⋊ C4×#455

Subgroups

subgroupG/H
centerC22#120×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#455C2
socleC22×C17C2×#120
prime radicalC2×C17×H(5,𝔽2)C22
cosocleC22×C4×C17C24
hypercenterC2×#455D17
hypocenterC17C4×#455
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

1442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 175454);