Finite Group Databasebeta

C4×#16837512 #28587171

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#16837512

Splittings

FittingC42×D4×C59 ⋊ C2
SylowC59 ⋊ C4×#442

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC42×D4×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
cosocleC22×C4×C59C24
hypercenterC42×D4D59
hypocenterC59C4×#442
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×D4

1326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 168050);