Finite Group Databasebeta

C22×#11763081 #17901708

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763081

Splittings

FittingC23×Q16×C17 ⋊ C2
SylowC17 ⋊ C22×#473

Subgroups

subgroupG/H
centerC23#10587624
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC23×Q16×C17C2
socleC23×C17#121
prime radicalC22×#63252C22
hypercenterC23×Q16D17
hypocenterC17C22×#473
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036952);