Finite Group Databasebeta

C2×#21421945 #28478368

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21421945

Splittings

SylowC59 ⋊ C2×#1283

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC22×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC2×C59×#431C2
socleC23×C59#95
prime radicalC24×C59C42
cosocleC2×C42×C59C23
hypercenterC2×#431D59
hypocenterC59C2×#1283
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59247);