Finite Group Databasebeta

C2×#29506299 #44500372

order30656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#29506299

Splittings

SylowC479 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic479
commutatorC22×C479C22×C4
FrattiniC2×C4C22×D479
Fitting, prime radicalC22×D4×C479C2
socleC22×C479C22⋊C4
cosocleC2×C4×C479C23
hypercenterC22×D4D479
hypocenterC479C2×#100
LCSG ▷ C22×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7664

Conjugacy classes & character table

4802 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 526);