Finite Group Databasebeta

C2×#21423207 #28564435

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21423207

Splittings

FittingC2×C59×#332 ⋊ C2
SylowC59 ⋊ C2×#1628

Subgroups

subgroupG/H
centerC23#14273697
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#332C2
socleC23×C59#120
prime radicalC2×#16837598C2
hypercenterC2×#332D59
hypocenterC59C2×#1628
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

1062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1154 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 145314);