Finite Group Databasebeta

C2×C4×#16814786 #44443031

order29504
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#16814786

Splittings

derived, SylowC461 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#14270406
commutator, hypocenterC461C2×C4×C8
FrattiniC22C22×#14270406
FittingC22×C4×C461C4
socle, prime radicalC23×C461C2×C4
cosocleC2×Dic461C23
LCSG ▷ C461
UCSC1 ◁ C22×C4

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1504);