Finite Group Databasebeta

C2×C4⋊#92418 #16839783

order3904
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊#92418

Splittings

SylowC61 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D61
commutatorC2×C61C22×C8
FrattiniC2×C4C22×D61
FittingC2×C42×C61C2
socle, prime radicalC23×C61C2×C4
cosocleC2×C4×C61C23
hypercenterC2×C42D61
hypocenterC61C2×C4⋊C8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 570);