Finite Group Databasebeta

C2×C4×#14273638 #28586013

order15104
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×C4×#14273638

Splittings

SylowC59 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC22×C42C2×D59
commutatorC2×C59C2×C43
FrattiniC22×C4C23×D59
FittingC2×C43×C59C2
socle, prime radicalC24×C59C22×C4
cosocleC22×C4×C59C24
hypercenterC2×C43D59
hypocenterC59C2×C4×#97
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C42 ◁ C2×C43

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166892);