Finite Group Databasebeta

C2×#21447511 #29832852

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447511

Splittings

SylowC61 ⋊ C2×#2134

Subgroups

subgroupG/H
centerC22C2×#14519692
commutatorC2×C4×C61C23×C4
FrattiniC2×Q8C23×D61
Fitting, prime radicalC2×C61×#535C2
socleC22×C61C2×#99
cosocleC2×Q8×C61C24
hypercenterC2×#535D61
hypocenterC61C2×#2134
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#535

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322407);