Finite Group Databasebeta

C22×C4⋊#6923 #16840824

order3904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊#6923
unambiguous semidirect productD61⋊(C2×C4⋊C4)

Splittings

FittingC22×C4×C61 ⋊ C4
SylowC61 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×#6923
commutatorC2×C61C23×C4
FrattiniC2C23×#6923
FittingC22×C4×C61C4
socleC23×C61C2×C4
prime radicalC23×D61C22
cosocleC2×D61C24
hypercenterC22×C4#6923
hypocenterC61C22×C4⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4

418 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, 1611);