Finite Group Databasebeta

C4×C22⋊#63216 #17960689

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C22⋊#63216

Splittings

SylowC17 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
centerC2×C42C2×#595
commutatorC2×C17C2×C4×C16
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC23×C17C22×C8
prime radicalC24×C17C2×C8
cosocleC22×#3622C23
hypercenterC22×C42#595
hypocenterC17C4×C22⋊C16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C22×C42

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095933);