Finite Group Databasebeta

C23×C22⋊(C59⋊C8) #29452116

order15104
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊(C59⋊C8)

Splittings

SylowC59 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D59
commutatorC2×C59C24×C8
FrattiniC2×C4C24×D59
FittingC25×C4×C59C2
socleC25×C59C2×C4
prime radicalC26×C59C4
cosocleC2×C4×C59C25
hypercenterC25×C4D59
hypocenterC59C23×C22⋊C8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 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, 1032995);