Finite Group Databasebeta

C2×#29506328 #44500822

order30656
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#29506328

Splittings

SylowC479 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#21440147
commutator, cosocleC8×C479C23
FrattiniC8C22×D479
FittingC2×Q16×C479C2
socle, prime radicalC22×C479D8
hypercenterC2×Q16D479
hypocenterC479C2×Q32
LCSG ▷ C8×C479 ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30656

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 976);