Finite Group Databasebeta

C2×C4⋊(C59⋊C8) #16837423

order3776
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊(C59⋊C8)

Splittings

SylowC59 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D59
commutatorC2×C59C22×C8
FrattiniC2×C4C22×D59
FittingC2×C42×C59C2
socle, prime radicalC23×C59C2×C4
cosocleC2×C4×C59C23
hypercenterC2×C42D59
hypocenterC59C2×C4⋊C8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 570);