Finite Group Databasebeta

C4×#11762818 #17032108

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11762818

Splittings

SylowC17 ⋊ C4×#419

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC22×C4×Q8×C17C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
cosocleC22×C4×C17C24
hypercenterC22×C4×Q8D17
hypocenterC17C4×#419
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×Q8

1586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167352);