Finite Group Databasebeta

C4⋊C8×D53 #16810642

order3392
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D53

Splittings

FittingC4⋊C8×C53 ⋊ C2
SylowC53 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D53
commutatorC2×C53C22×C8
FittingC4⋊C8×C53C2
socleC22×C53C22×C4
prime radicalC22×D53C2×C4
cosocleC2×C4×C53C23
hypercenterC4⋊C8D53
hypocenterC53C2×C4⋊C8
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1696

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3392, 568);