Finite Group Databasebeta

C2×#29506322 #44500810

order30656
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#29506322

Splittings

SylowC479 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D479
commutatorC2×C479C22×C8
FrattiniC8C22×D479
FittingC22×C8×C479C2
socleC22×C479C2×C8
prime radicalC23×C479C8
cosocleC8×C479C23
hypercenterC22×C8D479
hypocenterC479C2×M32
LCSG ▷ C2×C479 ▷ C479
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15328

Conjugacy classes & character table

7688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 964);