Finite Group Databasebeta

C2×#21423851 #28586192

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC2×#21423851

Splittings

SylowC59 ⋊ C2×#1747

Subgroups

subgroupG/H
centerC2×C8C4×Dic59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC2×C59×#405C2
socleC22×C59#376
prime radicalC24×C59#41
cosocleC22×C4×C59C24
hypercenterC2×#405D59
hypocenterC59C2×#1747
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C2×#405

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 167071);