Finite Group Databasebeta

C2×#29506373 #44500916

order30656
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#29506373

Splittings

SylowC479 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D479
commutator, cosocleC22×C479C24
FrattiniC22C23×D479
FittingC2×C4⋊C4×C479C2
socle, prime radicalC23×C479C23
hypercenterC2×C4⋊C4D479
hypocenterC479C2×#125
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30656

Conjugacy classes & character table

4808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 1070);