Finite Group Databasebeta

C2×#21425710 #28741362

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425710

Splittings

SylowC59 ⋊ C2×#2113

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC22×#131×C59C2
socleC23×C59C22×C8
prime radicalC22×#41×C59C4
cosocleC2×C8×C59C24
hypercenterC22×#131D59
hypocenterC59C2×#2113
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C22×#131

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322241);