Finite Group Databasebeta

#17981069

order4352
automorphism?
homologyAbelianization (H1) = C82 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

FittingC17×C22⋊C8 ⋊ C8
SylowC17 ⋊ #7016

Subgroups

subgroupG/H
centerC22(C2×#3633)⋊C4
commutatorC22×C17C82
FrattiniC22×C4C2×#3633
FittingC17×C22⋊C8C8
socleC22×C17#336
prime radicalC23×D17C42
cosocleC22×C4×#595C22
hypercenterC22⋊C8#3633
hypocenterC17#7016
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Polycyclic presentation:

2^8,17|a^2=d,b^2=e,d^2=g,e^2=h,b^a=bc,c^a=cf,d^b=df,i^b=i^9,i^e=i^13,i^h=i^16

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116313);