Finite Group Databasebeta

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C2×#14544945 #17970624

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14544945
unambiguous semidirect productD17⋊#1978

Splittings

FittingC22×D8×C17 ⋊ C4
SylowC17 ⋊ C2×#1978

Subgroups

subgroupG/H
centerC22#11763761
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC22×D8×C17C4
socleC22×C17#390
prime radicalC22×D8×D17C2
cosocleC2×C4×D17C24
hypercenterC22×D8#595
hypocenterC17C2×#1978
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

1694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105868);