Finite Group Databasebeta

C2×#29506318 #44500441

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

Aliases

direct productC2×#29506318

Splittings

SylowC479 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1916
commutatorC4×C479C22×C4
FrattiniC2×C4C22×D479
FittingC22×C8×C479C2
socleC22×C479C4⋊C4
prime radicalC23×C479Q8
cosocleC2×C4×C479C23
hypercenterC22×C8D479
hypocenterC479C2×#108
LCSG ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15328

Conjugacy classes & character table

7676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 595);