Finite Group Databasebeta

C2×#21427116 #28748222

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21427116

Splittings

SylowC59 ⋊ C2×#2361

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
Fitting, prime radicalC22×#121×C59C2
socleC24×C59C24
cosocleC23×C59C25
hypercenterC22×#121D59
hypocenterC59C2×#2361
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#121

4782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 329101);