Finite Group Databasebeta

C23×#10587479 #17897965

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#10587479

Splittings

SylowC17 ⋊ C23×#106

Subgroups

subgroupG/H
centerC25C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC23×C4⋊C4×C17C2
socle, prime radicalC25×C17D4
cosocleC2×C4×C17C25
hypercenterC23×C4⋊C4D17
hypocenterC17C23×#106
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

3614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033209);