Finite Group Databasebeta

C2×#14545860 #17982395

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

Aliases

direct productC2×#14545860

Splittings

SylowC17 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC23C22⋊#3633
commutatorC22×C17C2×C4×C8
FrattiniC23C22×#3633
FittingC23×C4×C17C8
socleC23×C17C22⋊C8
prime radicalC24×C17C2×C8
cosocleC22×#3624C23
hypercenterC23×C4#3633
hypocenterC17C2×#1377
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1117639);