Finite Group Databasebeta

C2×#14543884 #17960638

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

Aliases

direct productC2×#14543884

Splittings

FittingC23×C8×C17 ⋊ C4
SylowC17 ⋊ C2×#1395

Subgroups

subgroupG/H
centerC2×C4#10587539
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC22×C17#342
prime radicalC22×#63252C22
cosocleC2×#63252C23
hypercenterC23×C8#595
hypocenterC17C2×#1395
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095882);