Finite Group Databasebeta

C2×D4⋊#63216 #17958679

order4352
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×D4⋊#63216

Splittings

SylowC17 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC4×C17C22×C16
FrattiniC42C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C22⋊C8
prime radicalC22×D4×C17C8
cosocleC4×#3622C23
hypercenterC2×C4×D4#595
hypocenterC17C2×D4⋊C16
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093923);