Finite Group Databasebeta

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C4×#11763774 #17968140

order4352
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC4×#11763774

Splittings

SylowC17 ⋊ C4×#405

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C2×C43
FrattiniC23C23×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C23×C4
prime radicalC23×D17C22×C4
cosocleC22×Dic17C24
hypercenterC4×C4⋊C4#595
hypocenterC17C4×#405
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103384);