Finite Group Databasebeta

C2×#21443659 #29569537

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21443659

Splittings

SylowC61 ⋊ C2×#1279

Subgroups

subgroupG/H
centerC23×C4D244
commutatorC4×C61C2×C4×C8
FrattiniC2×C42C22×D61
FittingC22×C4×C8×C61C2
socle, prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC22×C4×C8D61
hypocenterC61C2×#1279
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

3952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59092);