Finite Group Databasebeta

C2×#14545861 #17982397

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14545861

Splittings

SylowC17 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC2×C4C22⋊#3633
commutatorC22×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC22×C8×C17C8
socleC22×C17#336
prime radicalC23×D17C2×C8
cosocleC2×#63242C23
hypercenterC22×C8#3633
hypocenterC17C2×#1377
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117641);