Finite Group Databasebeta

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C22×C4⋊C4×#595 #17978851

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4⋊C4×#595

Splittings

FittingC22×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC22×C4⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC22×C4⋊C4#595
hypocenterC17C22×C4×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4⋊C4

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1114095);