Finite Group Databasebeta

C4×#11763645 #17940937

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×#11763645

Splittings

FittingC2×C4×#41×C17 ⋊ C2
SylowC17 ⋊ C4×#585

Subgroups

subgroupG/H
centerC42C23×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC2×C4×#41×C17C2
socle, cosocleC22×C17C26
prime radicalC2×#11763645C2
hypercenterC2×C4×#41D17
hypocenterC17C4×#585
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C4×#41

11346 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, 1076181);