Finite Group Databasebeta

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C4⋊C8×D359 #37526462

order22976
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D359

Splittings

FittingC4⋊C8×C359 ⋊ C2
SylowC359 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D359
commutatorC2×C359C22×C8
FittingC4⋊C8×C359C2
socleC22×C359C22×C4
prime radicalC22×D359C2×C4
cosocleC2×C4×C359C23
hypercenterC4⋊C8D359
hypocenterC359C2×C4⋊C8
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

3620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 568);