Finite Group Databasebeta

C2×#14533327 #17203790

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14533327

Splittings

SylowC17 ⋊ C2×#2509

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C4×C4⋊C4×C17C2
socle, prime radicalC24×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17C2×#2509
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

1966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 339034);