Finite Group Databasebeta

C2×#21424389 #28589808

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21424389

Splittings

SylowC59 ⋊ C2×#1869

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C23×C8
FrattiniC22×C4C23×D59
FittingC22×C4×D4×C59C2
socleC24×C59C22×C4
prime radicalC23×D4×C59C4
cosocleC22×C4×C59C24
hypercenterC22×C4×D4D59
hypocenterC59C2×#1869
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

2438 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, 170687);