Finite Group Databasebeta

C4×#16837302 #28509873

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

direct productC4×#16837302

Splittings

FittingC2×C4×C22⋊C4×C59 ⋊ C2
SylowC59 ⋊ C4×#390

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC2×C4×C22⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C4×#390
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90752);