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D32×C4⋊C8 #11858221

order1152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD32×C4⋊C8

Splittings

FittingC32×C4⋊C8 ⋊ C22
SylowC32 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C23×C8
FittingC32×C4⋊C8C22
socleC22×C32C23×C4
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C22×C4⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

1349 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 92232);