Finite Group Databasebeta

C4×#97×D59 #28586010

order15104
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#97×D59

Splittings

FittingC4×#97×C59 ⋊ C2
SylowC59 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC2×C42C22×D59
commutatorC2×C59C2×C43
FrattiniC22×C4C23×D59
FittingC4×#97×C59C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenterC4×#97D59
hypocenterC59C2×C4×#97
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C4×#97

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166889);