Finite Group Databasebeta

C4×#11763617 #17898559

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#11763617

Splittings

FittingC4×C17×2−1+4 ⋊ C2
SylowC17 ⋊ C4×#577

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC4×C17×2−1+4C2
socleC22×C17C23×D4
prime radicalC2×#11763617C2
cosocleC2×C4×C17C25
hypercenterC4×2−1+4D17
hypocenterC17C4×#577
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×2−1+4

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033803);