Finite Group Databasebeta

#41×C4⋊#595 #17978981

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#41×C4⋊#595

Splittings

FittingC4×#41×C17 ⋊ C4
SylowC17 ⋊ C4⋊C4×#41

Subgroups

subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC4×#41×C17C4
prime radicalC2×#41×D17C22
cosocleC22×D17C25
hypercenterC4×#41#595
hypocenterC17C4⋊C4×#41
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×#41

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114225);