Finite Group Databasebeta

C2×#14543683 #17951541

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14543683

Splittings

FittingC22×C22⋊C4×C17 ⋊ C4
SylowC17 ⋊ C2×#1304

Subgroups

subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17#95
prime radicalC25×D17C22
cosocleC24×D17C23
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1304
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086785);