Finite Group Databasebeta

#135×#3622 #17003703

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

Aliases

direct product#135×#3622

Splittings

SylowC17 ⋊ C8×#135

Subgroups

subgroupG/H
centerC42D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC4×C17×#135C2
socleC22×C17C2×C4×D4
prime radicalC2×C17×#135C4
cosocleC42×C17C24
hypercenterC4×#135D17
hypocenterC17C8×#135
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#135

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 138947);