Finite Group Databasebeta

C2×#21422943 #28558206

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422943

Splittings

SylowC59 ⋊ C2×#1584

Subgroups

subgroupG/H
centerC22×C4D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC2×C59×Q8⋊C8C2
socle, prime radicalC23×C59C4×D4
cosocleC42×C59C24
hypercenterC2×Q8⋊C8D59
hypocenterC59C2×#1584
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 139085);