Finite Group Databasebeta

C23×#10587532 #17979401

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#10587532

Splittings

FittingC23×C8×C17 ⋊ C4
SylowC17 ⋊ C23×#97

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C23×C42
FrattiniC4C24×#595
FittingC23×C8×C17C4
socleC24×C17C42
prime radicalC24×D17C2×C4
cosocleC4×D17C25
hypercenterC23×C8#595
hypocenterC17C23×#97
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C23×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114645);