Finite Group Databasebeta

#41×Dic68 #17915797

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#41×Dic68

Splittings

SylowC17 ⋊ Q16×#41

Subgroups

subgroupG/H
centerC2×C4C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC8×#41×C17C2
socleC22×C17C23×D4
prime radicalC2×#41×C17D4
hypercenterC8×#41D17
hypocenterC17Q16×#41
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1051041);