Finite Group Databasebeta

C2×C22⋊#16814786 #44443043

order29504
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#16814786

Splittings

SylowC461 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#14270406
commutatorC2×C461C22×C8
FrattiniC22C22×#14270406
Fitting, prime radicalC24×C461C4
socleC23×C461C2×C4
cosocleC2×Dic461C23
hypercenterC24#14270406
hypocenterC461C2×C22⋊C8
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C23 ◁ C24

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1516);