Finite Group Databasebeta

C4×#16837325 #28510547

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#16837325

Splittings

SylowC59 ⋊ C4×#396

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC2×C4×C22⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C4×#396
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

1966 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, 91426);