Finite Group Databasebeta

C2×#21426309 #28743572

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

Aliases

direct productC2×#21426309

Splittings

FittingC2×C59×#361 ⋊ C2
SylowC59 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC22#16837719
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#361C2
socleC22×C59#481
prime radicalC2×#16837652C2
hypercenterC2×#361D59
hypocenterC59C2×#2238
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 324451);