Finite Group Databasebeta

C2×#28414192 #44443131

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

Aliases

direct productC2×#28414192

Splittings

SylowC461 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#14270406
commutatorC2×C461C22×C8
FrattiniC4C22×#14270406
FittingC22×C4×C461C4
socleC22×C461C2×C8
prime radicalC23×C461C8
cosocle#16814779C23
hypercenterC22×C4#14270406
hypocenterC461C2×M32
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C22×C4

90 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, 1604);