Finite Group Databasebeta

C2×C16×C22⋊D59 #28741837

order15104
isoclinismisoclinic class of Dic118
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×C16×C22⋊D59

Splittings

FittingC23×C16×C59 ⋊ C2
SylowC59 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C16C2×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingC23×C16×C59C2
socleC23×C59C22×C8
prime radicalC22×C22⋊D59C8
cosocleC2×C8×C59C24
hypercenterC23×C16D59
hypocenterC59C2×D4×C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C16 ◁ C23×C16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322716);