Finite Group Databasebeta

C4⋊C8×D43 #14582918

order2752
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D43

Splittings

FittingC4⋊C8×C43 ⋊ C2
SylowC43 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D43
commutatorC2×C43C22×C8
FittingC4⋊C8×C43C2
socleC22×C43C22×C4
prime radicalC22×D43C2×C4
cosocleC2×C4×C43C23
hypercenterC4⋊C8D43
hypocenterC43C2×C4⋊C8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 568);