Finite Group Databasebeta

D4×#16814786 #44443102

order29504
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#16814786

Splittings

SylowC461 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#14270406
commutatorC2×C461C22×C8
Fitting, prime radicalC2×D4×C461C4
socleC22×C461C22×C4
cosocleC2×Dic461C23
hypercenterC2×D4#14270406
hypocenterC461C8×D4
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1575);