Finite Group Databasebeta

C2×#21425737 #28741410

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425737

Splittings

SylowC59 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC2×C4#14273642
commutatorC23×C59C23×C4
FrattiniC2×D4C23×D59
Fitting, prime radicalC2×C59×#525C2
socleC22×C59C2×#99
cosocleC2×D4×C59C24
hypercenterC2×#525D59
hypocenterC59C2×#2120
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#525

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 322289);