Finite Group Databasebeta

C2×#21424047 #28587965

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21424047

Splittings

SylowC59 ⋊ C2×#1791

Subgroups

subgroupG/H
centerC2×C4#14273696
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#585C2
socleC22×C59#379
cosocleC22×C4×C59C24
hypercenterC2×#585D59
hypocenterC59C2×#1791
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#585

3662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 168844);