Finite Group Databasebeta

C22⋊C4×#63216 #17960752

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

Aliases

direct productC22⋊C4×#63216

Splittings

SylowC17 ⋊ C16×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×#595
commutatorC2×C17C2×C4×C16
FittingC4×C22⋊C4×C17C4
socleC23×C17C22×C8
prime radicalC24×C17C2×C8
cosocleC22×#3622C23
hypercenterC4×C22⋊C4#595
hypocenterC17C16×C22⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1095996);