Finite Group Databasebeta

#117×#3624 #17968673

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×#3624

Splittings

SylowC17 ⋊ C8×#117

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC23C23×#595
FittingC2×C17×#117C4
socleC23×C17C23×C4
prime radicalC24×C17C22×C4
cosocleC22×Dic17C24
hypercenterC2×#117#595
hypocenterC17C8×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#117

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1103917);