Finite Group Databasebeta

#595⋊#346 #17982373

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

unambiguous semidirect product#595⋊#346

Splittings

SylowC17 ⋊ C4×#346

Subgroups

subgroupG/H
centerC2×C8C2×#3633
commutatorC2×C17C42×C8
FrattiniC2×C4C22×#3633
FittingC4×C8×C17C8
socleC22×C17C2×C4×C8
prime radicalC22×D17C22×C8
cosocleC2×#63242C23
hypercenterC4×C8#3633
hypocenterC17C4×#346
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×C8

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Polycyclic presentation:

2^8,17|a^2=d,b^2=e,c^2=f,d^2=g,g^2=h,b^a=bh,i^a=i^9,i^c=i^4,i^d=i^13,i^f=i^16,i^g=i^16

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117617);