Finite Group Databasebeta

C2×#21422183 #28503555

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

Aliases

direct productC2×#21422183

Splittings

SylowC59 ⋊ C2×#1378

Subgroups

subgroupG/H
centerC2×C8(C2×D59)⋊C4
commutatorC22×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC22×M32×C59C2
socleC22×C59#336
prime radicalC24×C59C2×C8
cosocleC22×C8×C59C23
hypercenterC22×M32D59
hypocenterC59C2×#1378
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×M32

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 84434);