Finite Group Databasebeta

C2×C4×#14273695 #28747101

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×C4×#14273695

Splittings

FittingC22×C4×D4×C59 ⋊ C2
SylowC59 ⋊ C2×C4×#120

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC22×C4×D4×C59C2
socleC24×C59C24
prime radicalC22×#14273695C2
cosocleC23×C59C25
hypercenterC22×C4×D4D59
hypocenterC59C2×C4×#120
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

8582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 327980);