Finite Group Databasebeta

#124×#3622 #17042190

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#124×#3622

Splittings

SylowC17 ⋊ C8×#124

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D17
commutatorC22×C17C23×C8
FittingC4×C17×#124C2
socleC23×C17C23×C4
prime radicalC22×D4×C17C2×C4
cosocleC22×C4×C17C24
hypercenterC4×#124D17
hypocenterC17C8×#124
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×#124

974 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, 177434);