Finite Group Databasebeta

C2×#125×Dic59 #28747181

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#125×Dic59

Splittings

SylowC59 ⋊ C2×C4×#125

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC22×#125×C59C2
socle, prime radicalC24×C59C24
cosocleC23×C59C25
hypercenterC22×#125D59
hypocenterC59C2×C4×#125
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#125

2622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328060);