Finite Group Databasebeta

C2×#21422232 #28508874

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#21422232

Splittings

SylowC59 ⋊ C2×#1398

Subgroups

subgroupG/H
centerC2×C8C4×Dic59
commutatorC4×C59C2×C4×C8
FrattiniC2×C16C22×D59
FittingC2×C59×#346C2
socleC22×C59#346
prime radicalC23×C59M32
cosocleC2×C16×C59C23
hypercenterC2×#346D59
hypocenterC59C2×#1398
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C2×#346

222 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, 89753);