Finite Group Databasebeta

D59×Q128 #28509737

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

Aliases

direct productD59×Q128

Splittings

FittingC59×Q128 ⋊ C2
SylowC59 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC2D32×D59
commutator, cosocleC32×C59C23
FrattiniC32C22×D59
FittingC59×Q128C2
socleC2×C59C2×D32
prime radicalC2×D59D32
hypercenterQ128D59
hypocenterC59C2×Q128
LCSG ▷ C32×C59 ▷ C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ Q128

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90616);