Finite Group Databasebeta

← Prev (#17962914) Next (#17962916) →

C4×C4⋊C4×#595 #17962915

order4352
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC4×C4⋊C4×#595

Splittings

FittingC4×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C2×C43
FrattiniC23C23×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenterC4×C4⋊C4#595
hypocenterC17C42×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

2478 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, 1098159);