Finite Group Databasebeta

C4×C4⋊#14270406 #44443015

order29504
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊#14270406

Splittings

FittingC42×C461 ⋊ C4
SylowC461 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC2×C4C2×#14270406
commutatorC2×C461C2×C42
FrattiniC22C22×#14270406
FittingC42×C461C4
socleC22×C461C22×C4
prime radical, cosocleC22×D461C23
hypercenterC42#14270406
hypocenterC461C4×C4⋊C4
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

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, 1488);