Finite Group Databasebeta

C2×Dic1888 #28509739

order15104
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic1888

Splittings

SylowC59 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22D1888
commutator, cosocleC32×C59C23
FrattiniC32C22×D59
FittingC2×C59×C64C2
socle, prime radicalC22×C59D32
hypercenterC2×C64D59
hypocenterC59C2×Q128
LCSG ▷ C32×C59 ▷ C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3782 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90618);