Finite Group Databasebeta

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C4⋊C8×D509 #45655257

order32576
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D509

Splittings

FittingC4⋊C8×C509 ⋊ C2
SylowC509 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D509
commutatorC2×C509C22×C8
FittingC4⋊C8×C509C2
socleC22×C509C22×C4
prime radicalC22×D509C2×C4
cosocleC2×C4×C509C23
hypercenterC4⋊C8D509
hypocenterC509C2×C4⋊C8
LCSG ▷ C2×C509 ▷ C509
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16288

Conjugacy classes & character table

5120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 568);