Finite Group Databasebeta

C2×#21422047 #28497874

order15104
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422047

Splittings

SylowC59 ⋊ C2×#1327

Subgroups

subgroupG/H
centerC2×C4#14273642
commutatorC2×C4×C59C22×C8
FrattiniC2×M16C22×D59
FittingC2×C59×#423C2
socleC22×C59#324
prime radicalC24×C59M16
cosocleC2×M16×C59C23
hypercenterC2×#423D59
hypocenterC59C2×#1327
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#423

410 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, 78753);