Finite Group Databasebeta

#41×C22⋊Dic17 #17193529

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#41×C22⋊Dic17

Splittings

SylowC17 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
Fitting, prime radicalC23×#41×C17C2
socle, cosocleC23×C17C25
hypercenterC23×#41D17
hypocenterC17C22⋊C4×#41
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328773);