Finite Group Databasebeta

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C2×C4×C22⋊#3633 #17982879

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×C22⋊#3633
unambiguous semidirect product#595⋊(C2×C22⋊C8)

Splittings

FittingC23×C4×C17 ⋊ C8
SylowC17 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×#3633
commutatorC2×C17C22×C4×C8
FrattiniC22C23×#3633
FittingC23×C4×C17C8
socleC23×C17C22×C8
prime radicalC24×D17C2×C4
cosocleC22×#595C24
hypercenterC23×C4#3633
hypocenterC17C2×C4×C22⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118123);