Finite Group Databasebeta

C2×#14543829 #17960470

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

Aliases

direct productC2×#14543829

Splittings

SylowC17 ⋊ C2×#1376

Subgroups

subgroupG/H
centerC22×C4C4⋊#595
commutatorC4×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC23×C17C4⋊C8
prime radicalC24×C17M16
cosocleC22×#3622C23
hypercenterC23×C8#595
hypocenterC17C2×#1376
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095714);