Finite Group Databasebeta

C4×#11763576 #17897741

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#11763576

Splittings

SylowC17 ⋊ C4×#568

Subgroups

subgroupG/H
centerC42C23×D17
commutatorC2×C17C23×C42
FrattiniC2×C4C24×D17
FittingC2×C4×#41×C17C2
socleC22×C17C24×C4
prime radicalC22×#41×C17C22
cosocleC2×C4×C17C25
hypercenterC2×C4×#41D17
hypocenterC17C4×#568
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C4×#41

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1032985);