Finite Group Databasebeta

C2×Dic1952 #29601063

order15616
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic1952

Splittings

SylowC61 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22D1952
commutator, cosocleC32×C61C23
FrattiniC32C22×D61
FittingC2×C61×C64C2
socle, prime radicalC22×C61D32
hypercenterC2×C64D61
hypocenterC61C2×Q128
LCSG ▷ C32×C61 ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

3910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 90618);