Finite Group Databasebeta

C2×#14543844 #17960508

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14543844

Splittings

SylowC17 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC23#10587534
commutatorC8×C17C2×C42
FrattiniC2×C8C22×#595
FittingC22×C16×C17C4
socleC23×C17#107
prime radicalC23×D17Q16
cosocleC2×C8×D17C23
hypercenterC22×C16#595
hypocenterC17C2×#1381
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095752);