Finite Group Databasebeta

C2×#21424170 #28588419

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21424170

Splittings

SylowC59 ⋊ C2×#1819

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC23×C22⋊C4×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC26×C59C22
cosocleC24×C59C24
hypercenterC23×C22⋊C4D59
hypocenterC59C2×#1819
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C26 ◁ C23×C22⋊C4

3118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 169298);