Finite Group Databasebeta

C22×#11763685 #17968199

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11763685

Splittings

SylowC17 ⋊ C22×#341

Subgroups

subgroupG/H
centerC24C4⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC23×C8×C17C4
socleC24×C17C4⋊C4
prime radicalC24×D17Q8
cosocleC2×C4×D17C24
hypercenterC23×C8#595
hypocenterC17C22×#341
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

2238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103443);