Finite Group Databasebeta

#364×Dic17 #16949644

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct product#364×Dic17

Splittings

SylowC17 ⋊ C4×#364

Subgroups

subgroupG/H
centerC2×C8D4×D17
commutatorC4×C17C2×C4×C8
FrattiniC22×C8C22×D17
FittingC2×C17×#364C2
socleC22×C17C2×C4⋊C8
prime radicalC23×C17C2×M16
cosocleC22×C8×C17C23
hypercenterC2×#364D17
hypocenterC17C4×#364
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#364

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84888);