Finite Group Databasebeta

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C4⋊C8×D571 #49142285

order36544
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D571

Splittings

FittingC4⋊C8×C571 ⋊ C2
SylowC571 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D571
commutatorC2×C571C22×C8
FittingC4⋊C8×C571C2
socleC22×C571C22×C4
prime radicalC22×D571C2×C4
cosocleC2×C4×C571C23
hypercenterC4⋊C8D571
hypocenterC571C2×C4⋊C8
LCSG ▷ C2×C571 ▷ C571
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18272

Conjugacy classes & character table

5740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36544, 568);