Finite Group Databasebeta

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C4⋊C8×D499 #44543117

order31936
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D499

Splittings

FittingC4⋊C8×C499 ⋊ C2
SylowC499 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D499
commutatorC2×C499C22×C8
FittingC4⋊C8×C499C2
socleC22×C499C22×C4
prime radicalC22×D499C2×C4
cosocleC2×C4×C499C23
hypercenterC4⋊C8D499
hypocenterC499C2×C4⋊C8
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

5020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 568);