Finite Group Databasebeta

C2×#21445214 #29662370

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21445214

Splittings

SylowC61 ⋊ C2×#1674

Subgroups

subgroupG/H
centerC23#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#335C2
socle, prime radicalC23×C61#121
hypercenterC2×#335D61
hypocenterC61C2×#1674
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

1738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 151925);