Finite Group Databasebeta

C4×C4⋊#6923 #16840701

order3904
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊#6923

Splittings

FittingC42×C61 ⋊ C4
SylowC61 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC2×C4C2×#6923
commutatorC2×C61C2×C42
FrattiniC22C22×#6923
FittingC42×C61C4
socleC22×C61C22×C4
prime radical, cosocleC22×D61C23
hypercenterC42#6923
hypocenterC61C4×C4⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1488);