Finite Group Databasebeta

C4×#11763909 #17982435

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11763909

Splittings

SylowC17 ⋊ C4×#350

Subgroups

subgroupG/H
centerC2×C4C22⋊#3633
commutatorC4×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC4×D4×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC2×#63254C2×C4
cosocleC2×#63242C23
hypercenterC4×D4#3633
hypocenterC17C4×#350
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117679);