Finite Group Databasebeta

#135×#3624 #17966589

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct product#135×#3624

Splittings

SylowC17 ⋊ C8×#135

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
Fitting, prime radicalC2×C17×#135C4
socleC22×C17C2×C4×D4
cosocleC4×Dic17C24
hypercenterC2×#135#595
hypocenterC17C8×#135
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101833);