Finite Group Databasebeta

C2×#21422209 #28503621

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422209

Splittings

SylowC59 ⋊ C2×#1388

Subgroups

subgroupG/H
centerC2×C4#14273647
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC22×#108×C59C2
socleC22×C59#340
prime radicalC24×C59Q16
cosocleC22×C8×C59C23
hypercenterC22×#108D59
hypocenterC59C2×#1388
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84500);