Finite Group Databasebeta

C2×D8×#3624 #17966576

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D8×#3624

Splittings

SylowC17 ⋊ C2×C8×D8

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
Fitting, prime radicalC22×D8×C17C4
socleC23×C17C4×D4
cosocleC4×Dic17C24
hypercenterC22×D8#595
hypocenterC17C2×C8×D8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101820);