Finite Group Databasebeta

C2×#21422217 #28503644

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#21422217

Splittings

SylowC59 ⋊ C2×#1391

Subgroups

subgroupG/H
centerC2×C4#14273642
commutatorC23×C59C2×C42
FrattiniC2×#41C22×D59
FittingC2×C59×#408C2
socleC22×C59#342
prime radicalC22×#41×C59C22
cosocleC2×#41×C59C23
hypercenterC2×#408D59
hypocenterC59C2×#1391
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#408

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84523);