Finite Group Databasebeta

C4×#11763914 #17982468

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

Aliases

direct productC4×#11763914

Splittings

SylowC17 ⋊ C4×#364

Subgroups

subgroupG/H
centerC2×C4C4⋊#3633
commutatorC4×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC4×C8×C17C8
socleC22×C17C2×C4⋊C8
prime radicalC22×D17C2×M16
cosocleC2×#63242C23
hypercenterC4×C8#3633
hypocenterC17C4×#364
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117712);