Finite Group Databasebeta

C4×C8×C22⋊D59 #28587000

order15104
isoclinismisoclinic class of Dic118
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C8×C22⋊D59

Splittings

FittingC22×C4×C8×C59 ⋊ C2
SylowC59 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC2×C4×C8C2×D59
commutatorC2×C59C22×C4×C8
FrattiniC22×C4C23×D59
FittingC22×C4×C8×C59C2
socleC23×C59C23×C4
prime radicalC22×C22⋊D59C2×C4
cosocleC22×C4×C59C24
hypercenterC22×C4×C8D59
hypocenterC59C4×C8×D4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

1422 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, 167879);