Finite Group Databasebeta

C2×#14543697 #17957993

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#14543697

Splittings

SylowC17 ⋊ C2×#1312

Subgroups

subgroupG/H
centerC2×C42C2×#595
commutatorC2×C17C2×C4×C16
FrattiniC42C22×#595
FittingC2×C4×C8×C17C4
socle, prime radicalC23×C17C4×C8
cosocleC4×#3622C23
hypercenterC2×C4×C8#595
hypocenterC17C2×#1312
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093237);